Numbers and numerals

Axioms and arrays

Factors and multiples

Order of operations

Positive and negative numbers

Expressions, equations and inequalities

Angles

Classifying 2-D shapes

Constructing triangles and quadrilaterals

Coordinates

Area of 2-D shapes

Transforming 2-D figures

Prime factor decomposition

Conceptualising and comparing fractions

Manipulating and calculating with fractions

Ratio

Percentages

Different number systems

Sequences

Forming and solving equations

Forming and solving inequalities

Linear graphs

Accuracy and estimation

Algebra and problem solving

Ratio (8.6a)

Ratio, real life graphs, and rates of change

Direct and indirect proportion

Univariate data

Bivariate data

Famous maths problems

Angles and parallel lines

Angles in polygons

Bearings

Volume and surface area of prisms

Area review

Circles

FDP review (9.1a)

Probability

Sets and Venn Diagrams

Solving linear simultaneous equations algebraically

Solving linear simultaneous equations graphically

Angle review (9.5a)

Constructions, congruence, and loci

Pythagoras's theorem

Ratio review (9.7a)

Similarity and enlargement

Surds and trigonometry

Quadratic expressions (9.9)

Quadratic equations (9.10)

Indices and standard form

Growth and decay

Finance

Maths

Y8 Maths

Key Stage 3

Year 8

Statistics and probability

THEME

UNIT

In this lesson, we will look at the difference between univariate and bivariate data.

Univariate and bivariate data

﻿Hello everyone, it's Mr. Millar here. In this lesson, we're going to be looking at univariate and bivariate data. So first of all, I hope that you are all doing well. And just in case you haven't seen any of my videos on Oak before, my name is Mr. Miller, I'm a math teacher at a secondary school in central London. And yeah, I'm really excited to be doing these lessons for you, particularly because I'm really interested in this topic, which is statistics. Maybe you've already seen the lessons on the unit before on univariate data. This unit is going to be on bivariate data, so I really hope you enjoy it. Anyway, without further ado, let's have a look at the try this task. So Zaki and Cala have recorded height and weight data from 10 people. What's the same and what's different about their data sets? So write a sentence or two about what's the same, a sentence or two about what is different between these two data sets, Pause the video now for three or four minutes to have a think. Okay, great. Let's go through this. So first of all, what's the same is, of course, they are both recording height and weight. And what is also the same is that the data that they're getting is the same. So if you have a look at all the heights that Zaki has recorded, they're the same as all the heights that Cala has recorded. And the same with the weights. So that's what is the same, but there is an important difference here, which is that Zaki, of course, has recorded the heights and the weights separately, whereas Cala has recorded them together. And that is a really important difference because Zaki's got all this data, but he doesn't know, for example, the weight of someone who is 1.61 metres. Whereas a Cala does, so for example, the fourth person in her data, she knows is both 1.72 metres tall and 73.5 kilogrammes weight. So that's a really important difference. Can you think why it's more useful to have Cala's data? Why might that be more useful to have? Well it's more useful because if you were interested in looking at the relationship between height and weight, then you would want Cala's data because that would allow you to look at the relationship of those two, of those two things together. And it's this relationship between two different variables that we're going to be looking at across this unit. So let's have a look at the connect task. Okay. Let's have a read of this together. If we want to see if there is a relationship between two variables, for example, a person's height and weight, we need to record both variables for each data point. So first of all, this word variable, in case you haven't come across this before, it's a really important word in statistics. And what it means is it's essentially something that we can record or something that we can measure. So for example, in the previous slide, both the height and the weight were variables because we could record them or measure them. So in this task, what I want you to have about think about is what would you record if you wanted to explore what the most popular sport is, what the most popular sport is for different age groups, and so on. So what variables would you want to record to explore these three things? Write a sentence on each of these things. Pause the video now for two or three minutes to think about this slide. Okay, great. Let's go through this together. So the first one, what the most popular sport is, you would want to ask people what their favourite sport is. And that would get you some interesting results maybe. You might find that the most popular sport is, is tennis or football, or whatever. So that's what you would record. And this is typically called a univariate data because this is only one variable. So we are only recording one different thing here. Now, the second one, what the most popular sport is for different age groups, there are two different things that we need to record here. First of all, favourite sport. And second of all, age. So there are two things, two variables that we would need to record here, so this is what we call bivariate data. And bivariate comes from, the Latin word bi means two. So we are collecting the data on two different variables here, and this would allow us to, what would this allow us to discover? Well, this would allow us to discover the, the most popular sport is depending on how old you are. So maybe younger people prefer football. And if you're slightly older, you prefer cricket or something like that. So this would give us more data, or richer, richer data to have a look at. How about the last one? How much time people of different ages spend on social media? What would you record for this one? Well again, you would record age here because we're looking at different ages. And again, you would record time spent on social media. And again, that will give you a relationship between how old you are and how much time you spend on social media, which is really useful. So this may seem like a simple task, but this is just getting you to think about why it's important to record sometimes two different things. Let's have a look at the independent task. Okay, so this task needs some explaining. So it says here, describe in a sentence what each of the results of these data tables would be able to show you. So we've got four different data tables here. And for each one, I want you to write a sentence that would describe what the results of this table would show you. So for example, if we have a look at the first one here. Let's say that this table was completed. It doesn't matter what the results are, but let's just say a date, the data table was completed like this. What would this show you? Well, this would show you, you know, you could see that three people take the bus, one person walks, five people take the train. So it would show you the most common form of transports, most common form of transports. So this first table is only recording one thing and it would tell us the most common form of transport. You've got three more to do here. What would the results of each table show you? Pause the video, write down a sentence for each of these, four or five minutes. Pause the video now. Okay. So let's go through this and starting off with the one on the left-hand side, because it is the most straightforward, the journey duration in minutes and frequency. Well again, you're only recording one thing here. You're only recording how long the journey is. So again, this would tell you something like the most common length of journey. So maybe for example, you would find that that the most common form of journey is one that takes 11 to 15 minutes, and only one person has a journey of more than 20 minutes. Maybe that's what this would would tell you. The other two are a little bit more tricky because there are a number of things that are being recorded here. So let's first have a look at this one down here. So we've got different students and we are asking them for their journey duration and their journey length. So maybe student number one, their journey takes 10 minutes, and they're going two kilometres. Maybe student two is going for 25 minutes, and their journey is six kilometres. What would the results of this table show you? Well, there's actually a few things that this table could show you. So first of all, it would, you could work out the average journey time. You could work out the average journey length, and the most common journey time, the most common journey length. And so you could work out different pieces of data for both of these variables. But there's also something that you could have a look at if you looked at these two variables together. So if you looked at these two variables together, journey duration and journey length, you might be able to look at the relationship between them. So for example, is it true that longer journeys take a longer time? Maybe it's true, but this table would allow you to look at that, look at that relationship. And the final one, frequency by mode of transport and journey duration. Well, this time we're looking at four different modes of transport. So bus, walk, train, et cetera, how long does each take? And the results of this table, again, you could see the most common form of transport. You could see the most common journey duration, that kind of thing. But it would also tell you, for each mode of transport, how long does each journey take? So if, for example, you were interested in seeing which mode of transport had the shortest journey duration, this table set up would allow you to work that out. So what this is telling us is that, for these two starred tables, because we are recording more than one variable, it allows us, it would allow us to look at the relationship between those two variables. So it would allow us to tell us a lot more things. And this is going to be the focus of this unit. Let's have a look at the final slide, the explore task. Okay. Antoni is interested in finding out how the sun's intensity varies over time. He has a solar metre which can measure how strong the sun is at any given moment. He wants to take 20 recordings. What should he record? And what would you expect the findings to be? Okay. So just to make sure you understand this, we are interested in the sun's intensity, and we have got 20 recordings that we could take. So your job is to tell me what he should record. There might be, there's probably more than one thing you should look at here. So for each recording, you can, you can record more than one thing for each recording, just to make that clear. So anyway, there's more than one right answer, right answer here. So pause the video and have a think. Write down a couple of sentences. What would you record? What would you expect the findings to be? Okay, great. So let's talk through this. And there's a number of things that you could have said, and two things that I will go over. The first is that you could record the solar intensity at different times in the day. So maybe you were interested in finding out at what time the sun is strongest. But what you could do is you could record the solar intensity at, I don't know, eight o'clock in the morning, and then nine o'clock in the morning, at 10 o'clock, et cetera. And you might find that, you know, as you get later in the day, the intensity goes up because the sun is getting higher. And then maybe it's strongest at three o'clock, maybe something like that. And then after three o'clock, the intensity goes down. So in this case, you're recording two different things. You're recording the time of day and the solar intensity. So that is one thing that you could try. Another thing that you could try is, and maybe you've thought of this, but not necessarily recordings during, sort of, within each day, but you could, you might be interested in what time of year is the sun strongest. So is the sun strongest in June, or July, or August, or whatever? So if you were interested in that, you might do a recording each month. So here's May, here's June, here's July. And you might find that, you know, as you get into summer, the solar intensity goes up. And then maybe as you get into winter, it goes down again, something like that. But it's really important that if you decided to do this, you would need to record the solar intensity at the same time of day. Because if, for example, you took the intensity in May at three o'clock, but June at, at eight o'clock, then that would give you unreliable results. So it must be the same time of day. So again, you're recording two different variables here, the, the, the month, I guess, the time that, the month that you're recording and the solar intensity. And again, this would allow you to look at the relationship between the two things. So hope that this has whetted your appetite for the rest of this unit. Because looking at the relationship between two things is really the key of statistics. So allowing us to understand this is going to really help us out in the future. So anyway, thanks very much for watching today's lesson. That is all for today. Next time we're going to be looking at scatter graphs, so that's going to be really fun. So thanks very much for watching. Have a great day. See you next time. Bye-bye.

In this lesson, we will explore examples of scatter graphs to represent bivariate data.

Representing bivariate data

﻿Hello everyone, it's Mr. Millar here, and in this lesson we're going to be representing bi-variate data. So, first of all, I hope that you're all doing well, in this lesson we're going to be looking at how we represent bi-variate data by looking at scatter graphs. And before we have a look at any scatter graphs, here is the try this task. So are the following statements true or false? You need to look at the table on the left hand side, which has age of cars in years is in one column and price of the car in thousands of pounds in the other column. And you have got seven statements to decide if they are true or false. Pause the video now for four or five minutes, see how you get on. Okay, great, so let's have a look at these statements and go through them very quickly. So the first one at the table gives information on 20 different cars, well, this is false because each row of course represents a different car. So the first car is one year old and costs 6,000 pounds and in total there are 10 rows, so 10 different cars. Next one, the modal price of a car is 5,000. What we can see that we've got one, two, three fives here, which is the most number of fives so that is true. The range of ages of the cars is 10 years, well, this one is false, because the oldest car is eight years, and the youngest or the youngest car is zero years so the range is going to be eight. The brand new car costs 6,000 pounds more than the car, which is four years old. While, the brand new car is the one that is zero years old, so that is 10,000 pounds. The one wishes four years old is 4,000. So this one in the middle is true. The cars, which costs 4,000 pounds are the same age, well, no, one of them is four years old, the other one is five years old, so that is false. The two threes in the table have the same meaning. Well, this was false as well. Because one of the threes means three years old, the other three means at 3000 pounds. So they mean different things. And the final one, the value of the car decreases as the age increases. Well, this is an interesting one and this is what we're going to be coming back to. But if you said true, then I would agree with you because overall, if we have a look at the, the cars, which are for younger, they tend to have a higher value than the cars, which are older. But of course this isn't true for every single car, but in general, this seems to be the case. And this is, the key idea of for today's lesson, which is that if we have bi-variate data, we can use a scatter graph to look at the relationship between the two variables a lot more easily. Let's have a look at the next slide. Okay. So here was the connect slides and it says that representing binary data on a scatter graph can help us see connections more easily. So again, we have got a data table showing the age of car and the price of the car. And on the right hand side, we have got a scatter graph, which is showing that same data. And first of all, we can really easily understand what the scatter graph is showing. So we have got the age of Carl on the X axis and the price on the Y axis. So if, for example, we were looking at this point here, the one I've circled, we can see that the car, which is a six years old, has got a price of 4,000 pounds. So it's really easy to, to read off the graph, to read values off the graph. Now, the scatter graph is really interesting because it really clearly shows us a relationship between the two variables. So have a think, how would you complete this sentence here to describe the relationship between the age of the car and the price? Well, if you're thinking something like the scatter graph shows that as the age of the car increases, the price decreases then really well done, because you can see that as the age of the car increases, the price tends to go down. You could have also said the other way around. So as the age of the car decreases the price increases, that is absolutely right as well. But that is the key here. We can see that there was a relationship between these two variables and that is why a scatter graph is so useful. Now this is one other thing I want to say on the slide. And you could have seen it already that you've got this one point out here, this, car, which is seven years old and is more expensive than the others. And you could say, well, doesn't that mean that there isn't a relationship. And the answer to that is if we just have one piece of data, which is outside the rest of them outside of the trend, then we can say that this is an outlier and you might've come across that expression before an outlier. And what we say as well, yes, although this is outside of the other piece of data, we can, you know, we can ignore it or we can say it doesn't fit with the general trend. The general trend that the age of the car increases, the price decreases is still true, despite this an outlier. So anyway, hope that is very clear. Now let's have a look at the independent task. Okay. Let's look at the independent task now. So for this task, we've got a scatter graph showing the relationship between shoe size and height. And you have got five different questions to answer. So answer in four sentences. Pause the video now, for five or six minutes to have it go to at these five questions. Okay, great. Hopefully you had a good go at these. Let's go through them. So first of all, explain what point A means. Well, here is point A here and we can say, we can see that the shoe size is full and the height is 155 centimetres. So, that means that the person with a shoe size of four is 155 centimetres. Next one, what shoe size does the student who is 160 centimetres tall have, well, let's have a look where 160 centimetres is. We'll go across to this point here. And then we'll read down to a shoe size of six. Next one, what data point is the outlier? So the outlier is the data point, which is outside the general trends. And we can see that at this point here looks like it's outside the trends, because it's someone with quite a small shoe size who is quite tall. What fraction of the people in the sample have a shoe size of six or more? Well, we need to look at all the people that have a shoe size of six or more. So it would be all of these people. That's one, two, three, four, five, six, seven, eight, so eight people out of a total of eight, nine, 10, 11, 12, 13, and 14. So eight fourteens. And finally write a sentence, explaining what this graph is showing. Well, if you wrote something like in general, as the shoe size goes up, so does the height or as height increases? So does shoe size then, really well done. That shows this scatter graph is sharp. So anyway, I hope that you did well with these questions. Let's have a look at the explore task definition. Okay. So here is the explore task. And in this task, we have got three different scatter graphs. And that, each of these, what I want you to do is have a think about the different, the possible connections between the two variables. So what connection is there between age and height, between math test score and how far you can run and the number of photos taken and the battery life. So for each of these graphs, I want you to write one or two sentences explaining each of these. Pause the video now to give yourself time to do that. Okay, great. So let's go through these and for the first one, height and age, where we can clearly see that, as age increases, so does height. Which shouldn't be surprising because we know that as you get older, you grow, you get taller. So that is nice and straightforward. The next one maths test score and how far you can run. Well, we can kind of see in this one that the data is all over the place. There's no real clear trend in the data. And that shouldn't really surprise us because how far you run, and your test score in maths shouldn't really be related because there's going to be some people who are good at maths and can run really far. And also some people who are good at maths, you can't get very far. So there's no real relationship between the two of them. You can't really make a connection. But the final one you definitely can, because we can see that as the number of photos that you take increase your battery life decreases. Which shouldn't be a surprise because taking photos obviously takes up battery life. So we can expect that we have this relationship. And in the next lesson, we're going to be taking this a little bit further, because what this comes down to is this idea of correlation. So two variables are correlated. There's a relationship between them. So we're going to have a look at that in the next lesson, but as for today, that is it. So thanks so much for watching. Well done for completing this video, hope you enjoyed it. See you next time, have a great rest of your day. And bye bye.

In this lesson, we will investigate different kinds of correlation and interpret them from scatter graphs.

Correlation

﻿Hello everyone, it's Mr Millar here. In this lesson, we're going to be looking at correlation. So first of all, I hope that you are all doing well, and in the last lesson, we looked at scatter graphs as a way of representing bivariate data. And we saw that scatter graphs were really useful for seeing the relationship between two variables. In this lesson, we're going to take it a step forward, by having a look at what we call correlation, which is essentially how we describe the relationship that we see between the two variables. And correlation is a really important word, and if you ever read the newspapers, or read any kind of scientific journal, or anything like that, you will see this word, correlation, come up a lot, so it's a really important word, and we're going to find out wat it means, but first of all, let's have a look at the try this task together. So, here we've got a scatter graph, showing the relationship between the number of photos and battery life, and what I want you to do, is think about how could you describe the connection between the variables shown on the scatter graph? And also, how many ways can you complete the sentence frame below, so pause the video now, to have a go at thinking about these two questions. Okay, great, so we actually saw this scatter graph at the end of the last lesson, or at some point last lesson, and as we see, that as we take more photos, the battery life decreases, which makes sense, because taking photos on a camera uses up battery life. So, that is what is going on here, and in terms of the sentence frame, we can either say, "As the number of "photos "increases, "the battery life "decreases." Or we could say it the other way round. So, "As the number of photos decreases, "the battery life increases." So, that is the try this slide. Now, let's have a look at this idea of correlation. Okay, so, for this connect slide, we have got three different scatter graphs, that each show a different type of correlation. Positive correlation, negative correlation, and no correlation. Now, the first one, positive correlation, says, "As one variable increases, so does the other." So the example here is that, as cinema attendance increases, so does the amount of popcorn sold. The next one, negative correlation, well, that says that, "As one variable increases, "the other one decreases." So, the more days you're absent from school, the lower your average test score will be, for example. And the final one, no correlation, is also really important. And that is when there is no apparent pattern between the two variables. So, for example, if we look at the distance that a pupil lives from school, and their score in the test, well, there shouldn't be any pattern, any relationship between those two things, so as we can see, the data points are kind of all over the place, there is no clear pattern. And it's also worth pointing out that when we see a positive correlation, we can see that there is a positive gradient. If we imagined a kind of a straight line, sort of connecting these points together, there'd be a positive gradient, and the same is true for a negative correlation, there would be a negative gradient. The other thing that I wanted to point out here is that we can have a different strength of correlation. So, for example, in the first one, we would say that there is a strong positive correlation, because, if we imagine a straight line connecting all of these points, something like this, then all of the data points are very, very close to that line, so there is a strong positive correlation. If, however, we had a graph that looks a little bit more like this. Well, we would say that there is still a positive correlation, because as one variable increases, so does the other, but this one is a much weaker positive correlation, because the data points are not so close together. So, positive correlation is when, as one variable increases, so does the other, but it can either be stronger or weaker, depending on how close the data points are together, or how close the data points are to a line of best fit, going through them. Anyway, make sure that you have got these three definitions down, before we move on to the independent task. Okay, so, two questions for you to have a think about here. The first one says, "Write a sentence explaining "what each graph is showing, and the type of correlation." So, two graphs for you to have a think about, and the other one says, "On each set of axes, "plot eight to 10 points, based on the correlation "that you would expect to find." So, for example, the first one, the hair length and maths test results, well, you wouldn't expect any kind of relationship between the two of them, so you might expect, you'd expect there to be no kind of correlation, so you would plot your points kind of like that, all over the place. There's no pattern. Hope this is clear, pause the video now, four or five minutes, to have a go at these questions. Great, well done, let's go through it. So question one, first of all, well, clearly there is a positive correlation here, because the more hours the heating is on, the higher the heating bill would be, which is pretty straightforward. And we can see here that there is a very strong positive correlation here, because the data points are very close together, they're very close to the line of best fit. And the next one, the test score versus distance, well, there doesn't seem to be any kind of pattern here. We would say that there is no correlation for that one there. And for question two, well, we've done the first one already. There'd be no correlation between the maths test results and the hair length, but for the other ones, we would expect to see a correlation, so, ice cream sales versus temperature, well, clearly the hotter it gets, the more ice cream we'd expect to sell, so we'd expect, say, a positive correlation like that. You could argue that it might be a very strong positive correlation, it might be slightly weaker, so it really depends on what you think, because obviously the number of ice cream sales might depend on other things, not just temperature. The next one, time spent brushing teeth versus number of cavities. Well, clearly the longer you spend brushing your teeth, the fewer cavities you would expect to have, so make sure that you brush your teeth, so, we'd expect a negative correlation, to look a bit like that. The final one, height versus shoe size, excuse me. Well, clearly, the taller you are, as you grow in height, so you would expect to grow with your shoe size, so we'd expect a kind of positive relationship here as well. Anyway, that is that, hope that you found that nice and straightforward. Now let's have a look at the explore task. Okay, so, explore task, we have got eight different graphs here. So first of all, you need to sort these graphs into groups, based on the correlation shown. So, let's call these graphs A, B, C, and D. E, F, G, and H. So sort these graphs into different groups, based on the correlation, and then place them in order by strength of correlation. So remember what we said. If the correlation is strong, then the data points are close together. If the correlation is weak, then they're further apart, and finally, think of variables that might match each graph. So, for example, the second graph might be, you could have the one that we had already about the number of hours that the heating bill is on, compared to the cost of the heating bill. Okay, pause the video now, five or six minutes to have a go at this explore task. Okay, great, let's go through these. So, first of all, let's have a look at, let's have a think about the ones that are a positive correlation. So, a positive correlation, whether, as one variable increases, so does the other, well, A is definitely positive, B is definitely positive, and so is E, I would say. But I would definitely say that, looking at E, compared to A and B, E has a much weaker positive correlation, because the data points are further apart. What about a negative correlation? Well, definitely D, definitely G, and definitely H. And I don't think any of the other ones have a negative correlation as well. Now clearly D and G have a very strong negative correlation, and H, well, H is a bit of an interesting one, because if you imagine plotting a line, you couldn't really plot this straight line between those points, so you might need a little bit of a curved line, which is interesting, but they definitely all have a negative correlation. And then finally, no correlation, well, that is going to be C, that is going to be F, as well. So, and in terms of the variables, that might match each graph, well, that is really up to you. For example, for G, you could have temperature here, on the X axis, so, as it gets hotter, what goes down? Well, what might go down is your heating bill, because you don't need to put the heating on, if it's hot, whereas if it's cold, you need to put the heating on, so your heating bill would be bigger. That might be one example, but I hope that you found lots of interesting examples yourself. Okay, that is it for today's lesson, where we have looked at different kinds of correlation. Next time we're going to be extending our learning to be looking at lines of best fit. So that is it for today, thanks very much for watching, and see you next time, bye-bye.

In this lesson, we will learn how to draw lines of best fit on scatter graphs, and we will invesitgate the purpose of lines of best fit.

Lines of best fit

﻿Hello everyone. It's Mr. Millar here. In this lesson, we're going to be looking at lines of best fit. So first of all I hope that you are all doing well. And last lesson, we looked at this idea of correlation between two variables. So we looked at positive correlation, negative correlation and no correlation. I also mentioned last lesson a couple of times about this idea of lines of best fit. And in this lesson, we're going to look at that in more detail. But anyway, to start off with, let's have a look at the Try this task. So here we have got three different scatter graphs. First of all, what's the same, and what's different between these three graphs? And second of all, can you come up with some examples of pairs of variables that fit these graphs? So pause the video for three or four minutes, write down a couple of sentences, and then we will have a look through. Okay, great. So let's talk through it. So first of all, what's the same? Well, in each of these cases, we have got a positive correlation, which we had looked at last time. So what was the correlation means is that as one variable goes up, so does the other. So what's different? Well, you could have a thought of a couple of things here. First of all, in the first two examples, we can see that all of the points are quite close together. So we would say that this is quite a strong positive correlation in these two cases here. And the third case, there's still definitely a positive correlation because we can see that as one variable increases so does the other, but the correlation isn't quite as strong because the points are fairly spread out. So we would say that this is a fairly weak positive correlation. Also what you could have been thinking that's different is that if you imagine drawing a straight line that fit these points as best as possible, you would find that they would intersect the X or Y axis at different places. So for example, the one in the top right, you can imagine that if you drew a straight line, I'm not going to use a ruler, but if you were using a ruler to do a straight line like this, it would hit the Y axis here. Whereas for this one, it actually hits the X axis down here. And this one here would maybe go something like this and hit the Y axis like that. So they all have a different intercept. And finally, some examples of pairs of variables. Well, for the first two, you need to think what two variables would be very strongly correlated. So for example, you might have a think that the amount of time that the heating is on compared to the heating bill would give you a very strong positive correlation. A slightly weaker positive correlation might be, for example, the amount of time spent studying for a test and the score on that test. Clearly, if you study more you're likely to do better, but, you know, some people might get away with not studying so much. So you might expect to see a slightly weaker correlation there. Anyway, let's move on now to the Connect task. Okay. So here is the connect task. And in this scatter diagram, we have got the temperature outside against the number of ice creams sold. Now, what we can do, I've done this a few times already, is we can draw a line of best fit going through the data and it would look something like this. So a couple of points to mention first of all. First of all, it is a nice straight line and it's one straight line so it doesn't kind of zigzag around going between the data points. So if you draw your line of best fit like that, which sometimes might happen. Definitely don't do that because you don't want to connect all the points together. You want one nice straight line that is the best fit between those points. The other thing to notice is that the line I've drawn, you've got approximately the same number of pieces of data above that line compared to below that line. So if I look at the point above that line, we've got one, two, three, four, five, six, and you've got approximately the same number below that line. So that is the second point to mention. And the third point we talked about this idea of an outlier last lesson. So down here, you know, it was a very hot day, but not many ice creams were sold. Maybe that's because it was hot, but also rainy. Sometimes that happens. Mainly because the ice cream van didn't turn up till later, who knows? But anyway, when you're thinking about the line of best fit, you don't worry too much about that outlier. The line of best fit you're thinking what's the correlation overall? What does the data look like overall? Let's draw the best possible line to go through it. Anyway, that is how we draw the line of best fit and it's useful for a number of reasons. First of all, number one, it more easily... You can more easily see what the correlation between the data is as we talked about already. Second of all, it helps us identify the outliers. So any outliers like this one down here would be a long way away from the line. And third, we can work out an expected relationship. So let's talk through what does that mean? Work out an expected relationship? Well, let's have a look at what the first student is saying here, he's saying "I would expect that if it was 20 degrees out, "blank, ice creams would be sold." So what do you think? What would go in that missing gap there? Well, it turns out that we can use the line of best fit to work out an expected relationship between the temperature and the ice creams sold. So say for example, if it was 20 degrees out, we would follow up the line, follow up the graph up to the line until we get to there and then see what number of ice creams that gets to, and we can see it gets to 40 ice creams. Now that's not saying for sure that if it were 20 degrees out we would definitely sell 40 ice creams. And the reason why we can't say that for sure is because the relationship isn't exactly perfect. But we can say that we might expect that to be 40 ice creams by looking at the line of best fit. So really important that the line of best fit is helpful for a number of reasons including predicting or expecting what might one variable might be If we know another. Let's now have a look at the Independent task. Okay. So three questions to have a look at here for the independent task. The first question says, which of these lines of best fit is the most appropriate to use. So we've got three different lines. The data is the same in all three graphs, but you need to decide, which is the best line. Second, use your line the best fit to predict the value of a car which is seven years old. So whichever line of best fit that you think in question number one is the best to use. Use that one to predict the value of the car, which is seven years old. Third, state which car is an outlier. Pause the video, it shouldn't take you any more than a couple of minutes to do these three questions. Okay, great. So let's go through this. The first question, well, if you're thinking that the third line of best fit is the best, then well done. Why is that? Well, we definitely don't want the second one because as we said before, we want it to be one nice straight line. What's wrong with the first one? Well, if you have a look at the number of points above the line compared to below the line, there are many more points here below the line compared to above the line, so we don't want that. The third one is the best one, because we've got a nice straight line of best fit through the data with the same number of points above and below it. Second, use your line the best fit to predict the value of the car which is seven years old. So we're going to use the third line of best fit that we decided was the best. We're going to find at seven years old, which is around here, we're going to go up to our graph and we see that the value is 4,000 pounds. Finally, state which car is an outlier. Nice and easy, it's this one up here, which it looks like it's seven years old and 14,000. That is definitely an outlier. Okay. In the explore task, we're going to have a look to see why these lines of my fit might not always be perfect. So let's now have a look at the Explore task. Okay. So, Zaki collects data about the height and shoe sizes of some of his class. What do you think of his statements? Draw a scatter graph and line of best fit to help you decide. So here we've got 15 different pupils from A to O, and for each one at Zak has recorded the shoe size and the heights. And he is making two statements about that. What you need to do is first of all, draw a scatter graph using if you have it, some graph paper, if you don't have it you can use normal paper. If you're not able to draw the scatter graph, then on the next slide, I will show you the scatter graph. So pause the video now if you're able to draw a scatter graph. if not, I will show you a scatter graph in a second. Okay. So here is the a graph that reflects the points in the table on the previous slide. So if you did manage to plot the scatter graph well done. This is what it should look like. If not, now is your time to have a think about the two statements that Zaki is making. So I would expect someone 157 centimetres tall to have size seven shoes. And someone hang in 35 centimetres tall to half the size size zero shoes. Pause the video if you haven't already to write down a sentence which will fit each of these statements. Okay, great. So well done for doing that. Let's think about the results. So first of all, if I were to plot a line of best fit going through the data, I would plot something like that, where I can see that there are roughly the same number of points above the line compared to below the line. And if I looked at my first statement, well, I can see someone who is 157 centimetres tall, would be around here on my graph. And I could see that roughly they would have a shoe size of seven. So I would agree with this statement and I would agree with it because I feel comfortable saying, "Okay, if my height was 157 centimetres, "I might have a size seven shoes." So that one I agree with. But the second one, I would be much more capital about. And can you have a think why? Can you think why I drew my line of best fit like this, rather than like this? Well, the reason why I only extended it to here and here was because that is roughly where the data I recorded lay. So I don't feel comfortable, extending my line of best fit to above and below the data that I looked at. And the reason that I don't is because the relationship between the two variables might look very different. For example, if you looked at the shoe sizes and heights of some adults, maybe some adults are, you know, 180, 190 centimetres tall, and the graph would tell us that if someone was 190 centimetres tall, they might have size, I don't know, size 15 shoes. But we know that there's very few people who have shoe sizes that big. So you might not feel comfortable extending the graph for higher... Higher heights. The same is true when you think about extending the graph below a height of around 150 centimetres. You haven't collected the data, so you shouldn't necessarily feel comfortable extending that line of best fit. Because for example, someone 135 centimetres tall, well, not many people have a size zero shoe. That may not even be possible. So I would not feel comfortable with this statement. So what this tells us is that you need to be careful with your lines of best fit because they may not always follow the same pattern if you extend it beyond the data that you have already gathered. So you always need to think, does this make sense? Is it realistic to do this? Okay. That is it for today's lesson. Hope you've enjoyed it. And I will see you next time. Thanks so much for watching. Have a great day and bye bye.

In this lesson, we will investigate the relationship between causation and correlation.

Correlation and Causation

﻿Hello everyone, it's Mr. Millar here. In this lesson, we're going to be talking about correlation and causation. So, first of all, I hope that you are all doing well, and over the last few lessons, we've been looking at scatter graphs and this idea of correlation and lines of best fit. So for the Try This task, we have got a scatter graph with some points plotted on it, and we've got a line of best fit as well. And as Zaki's statement is saying, "This graph shows that book sales cause car accidents." So what do you think, do you think that this statement is true or false? Why or why not? What I want you to do is pause the video for one minute to write down a couple of sentences about the statement. Pause the video now. Okay, great, so I hope that you all said that Zaki's statement is incorrect. And that clearly is incorrect, because the idea of higher book sales causing car accidents is clearly ridiculous. There is no way that if more books are sold, then that causes car accidents. That's just not true. But what is interesting here is that clearly the scatter graph shows that there is a positive correlation. So, well done if you mentioned positive correlation in your answer. So the graph does show that as the number of car accidents goes up, so does the number of book sales, but just because there is a positive correlation here does not mean that one causes the other. And it's this point that we are going to be talking about in more detail for the rest of this lesson. So when you're ready, let's move ahead to the Connect slide. Okay, so let's have a look at the Connect slide now, which says correlation doesn't necessarily mean causation. So as we saw on the last slide, just because two things happen to be correlated, it doesn't mean that there is any causation going on here. Okay, so underneath here there are three statements, and in each of these statements there is a correlation, either a positive correlation or a negative correlation. So I want you to pause the video, to write down a sentence or two on each statement. And what I want you to think about is is there any causation going on here? What is going on behind the following correlations? Pause the video for two or three minutes, one sentence on each of these statements, pause the video now. Okay, great, let's go through these statements, then. So the first one, "There is a positive correlation between lung cancer and smoking." And if you've studied this before, you would definitely know that this is true. And what is going on here? Well, clearly the fact is that higher rates of smoking, if you smoke, you are more likely to develop lung cancer. So there is a causal relationship here. There is some causation happening because smoking causes your chances of getting lung cancer to be higher. So there is a time correlation going on here. The next one, "There is a negative correlation between temperature and heating bills." Well, again, there is definitely some causation going on here because if there are higher temperatures, so if the temperature is higher, that means that because it's warmer out, you have the heating on less. And if you have the heating on less, obviously your heating bill is going to be lower. So the first two statements, there is a correlation going on and there is also causation. What about the third one? Well, there is a correlation again here, because when you have a look at the number of ice creams sold and number of barbecues, you would see that when there are more ice creams sold, there are more barbecues, but is there causation here? Does more ice creams sold lead to more barbecues or do more barbecues lead to more ice cream sold? Well, I don't think so. I think that there is not necessarily any causation going on here. And what is going on here, of course, is that when it is hot out, then you would typically see more ice creams sold and more barbecues, so it's something else that is causing both of these things to increase at the same time or decrease at the same time. So just because there is correlation here, it does not mean that one thing is causing the other. It's also worth pointing out that for the first two statements, the causation only goes one way. So we say that smoking causes lung cancer, but we wouldn't say that lung cancer causes smoking, and the same thing for temperature and heating bills. Sometimes there is causation both way, we do see some examples of one thing causing the other, and then the other thing causing the other thing, it's kind of this circular loop, but not necessarily. So hope that is nice and clear. Let's now move on to the independent task. Okay, so for the independent task question one, you have got five different boxes here. In each box, there are two variables, and I want you to do two things here. First of all, decide if you think these variables are correlated. So is there positive correlation, negative correlation or no correlation? And second of all, explain whether there is any causation going on here. So maybe there is some causation, maybe there isn't, it's up to you. The second question shows a scatter graph between cheese consumption and number of the PhDs awarded, and there's a statement about cheese makes you clever, so I want you to see if you agree with that statement. So pause the video, five or six minutes, to write down some sentences for these two questions here. Okay, great, so let's go through these questions. So the first one we'll go through them very quickly. Your last math test score and how far you can run. Well, I doubt that there's any correlation going on here and also no causation as well. Next one, height and age of secondary students. Well, hopefully you said that there is a positive correlation because if you're taller, you're more likely to be older. And what about the causation here? Well, clearly it is age causing height because as you grow older, you grow taller. So definitely age is causing high here. Next one, age of the car and price of the car. Well, we've seen this one in a lesson a few lessons ago. There is negative correlation typically here. And you know, because as the age of the car gets older, the price goes down. So here, the causal relationship is as the age increases, the price of a car typically goes down. So there is negative correlation and causation here as well. Next one, number of ice creams sold and air temperature. That's nice and obvious. The higher the temperature, the more ice creams sold, so a positive correlation here, and air temperature causing ice creams sold to be higher. The final one, distance you live from school and the time it takes you to get to school. Well, again, you should have said a positive correlation here and clearly the longer you live from school, the more time it's going to take you to get to school, so there's causation going on here. So actually for all of these, excuse me, all of these four statements where we had some correlation, there is also a causation going on here, but this is not always the case. For example, in question two, we can see a positive relationship between cheese consumption and the number of PhDs awarded, but just because there is positive correlation, does that mean that there is causation here? So is the statement, "Cheese makes you clever," true? Well, hopefully you said that this is very unlikely because clearly there are other things going on here, it's not the case that cheese makes you clever, it's definitely not the case. So how have a think about the second question here, what could cause this positive correlation here? Why do you think this is happening? Well, one reason might be that if you are wealthier, you are more likely to have a PhD. And also if you're wealthier, you're more likely to eat more cheese. That could be one thing that is behind this positive correlation, but there is definitely no causation going on here. So anyway, let's now have a look at the Explore task. Okay, in the Explore task, we have got five variables below: cycle ownership, greenhouse gas emissions, et cetera. So, first of all, what correlation would you expect between each paring and why, and which do you think might have a causal link? So for example, you might expect there to be a positive correlation between cycle ownership and cycle use. So the causal relationship would be that, you know, the more likely you are to own a bicycle, the more likely you are to use it. So the causal relationship would run this way like that. That could also be, you could also have more than two variables in a chain, so you could start off by saying more cycle ownership leads to more cycle use, but that, in turn, could lead to something to do with car use. So feel free to have a think here about the relationship between these five pairings. Okay, great, so hope that you wrote some interesting things down here, and we can just talk about this for a second. There's lots that we could talk about here, because it's a very interesting topic, but typically, if you think about it, people have a choice about how they get around. So they could use a car, they could use a bicycle. And so if you own a bicycle, you're more likely to to use it, as we've said. And then also if you use your bicycle more, this is likely to lead to your personal car use going down. And if your personal car use goes down, then we know that when you use a car, that is a source of greenhouse gas emissions, so greenhouse gas emissions could go down, but not necessarily, of course, you know, there might be a causal relationship between the amount that you use your car and greenhouse gas emissions, but just because there might be a causal relationship, it doesn't necessarily mean that there's going to be correlation because, let's say, for example, that fewer people use their cars to get around, but at the same time, I don't know, more people are turning on their electricity or their heating, that would lead to more greenhouse gas emissions. So there's lots of things that affect greenhouse gas emissions, not just car use. So anyway, that is it for today's lesson. Hope you've enjoyed it. It's a really important one to think about the link between correlation and causation. So the message really is that when you see correlation, you have to think really carefully about what is causing this correlation, because just because there is a correlation, doesn't mean that one variable is causing the other variable to change as well. So anyway, thanks very much for watching, that is it for today, and I hope you enjoyed it. Have a great day and see you next time. Bye-bye.

In this lesson, we will discuss the benefits are potential problems of truncating axes.

Truncating axes

﻿Hello everyone, it's Mr. Miller here. In this lesson, we're going to be looking at Truncating Axes. So first of all, I hope that you are all doing well, and it's going to be a shorter lesson today. So let's get right to it with the try this task. So, do you agree with Anthony why? or why not? He's saying that chart B shows that fewer buses were on time , as the bar is smaller. So, obviously you're going to have to look at charts A and B on the right hand side, and write down a sentence or two explaining whether you agree or disagree and why you have made that decision. Pause the video for 30 seconds to one minute right now. Okay, great, let's go for it. And if you disagreed with him, then really well done. Because, although it looks like the bar for on time is smaller in B, actually the graphs are showing the same in both cases, because what you need to do is not look at the size of the bar, but you need to look at where the bar goes along to on the axis. So for example, for chart A, you can see that the late buses is 60 and the on time buses is 40, and it is the same in chart B. We have 60 and we have 40. So exactly the same thing is going on here. So you may ask why, what is going on, what's happening here? And, if you spotted this thing down here, then that is the reason for it. So, in chart A, you can see that the Y axis starts at zero, whereas in chart B there's this little squiggle, which means that the axis is not going to start at zero. And you sometimes see this when we have what we call truncated axes. Truncated basically means shortened. So, you can see that the Y axis in chart B has been shortened, because instead of starting at zero, it starts at 30. So this whole lesson is going to be about truncating axes. And the whole point of it is that you need to be really careful whenever you are reading off graphs. You need to check with the scale on the axes. I think it's an important topic because often some people try to manipulate their data by truncating the axes. Famously, it happens quite a lot in politics where there might be a bar chart showing, you know, an opinion of poll or who's going to vote for what party. And one party may change the scale on the axes so that it looks like they're more popular than the others or something like that. So it's something to be aware of. And we're going to have a look at this in this lesson. Let's now go onto the connect slide. Okay, so a very quick one. This is really just covering the same thing. So truncating axes can help to see data differences and detailing the data points more clearly, but we need to be careful when reading data in this way. So what this is saying is that truncating axes can actually help us. And we're going to see in a couple of slide's time where they might help us, but we do need to be careful when reading the data such as in this example here. So, we've already kind of covered this, but pause the video one or two minutes, read Anthony's statement and explain why he is incorrect. Well, of course he's incorrect because he didn't read the scale on the axes. And the scale on the axes again gives me 60 and 40. So it's not the true, it's not true that a triple the amount of buses were late than on time. That even though it might look like it, 'cause we'd go up to two bars here and we'd go up six bars here, but it's not actually the case that a triple the number of buses were late because we need to be careful with the scale on the axis. Let's now move on to another example in the independent task. Okay, so here we have got another chart where the axis has been truncated, truncated. Again, it's on the Y axis but it's worth pointing out that we do sometimes see this on the X axis as well. And sometimes even we see a truncation happening on both axes. Anyway, here are some questions for you to have a think about, true of false, pause the video three or four minutes, and work out the answers to these questions. Great, so this should be nice and straightforward. And, what you should have done is you should have read off the values before attempting these questions. So, first of all, September had more than doubled July sales. Well, if we read off September, we get to 27 here and July, we get to 23. So we're comparing 23 to 27. So actually it's actually quite close as they need a 4,000 difference. It's certainly nowhere near more than double. So this is definitely false. So it kind of was the best month of the year. Well, this is very obviously true because even though we have truncated the axes, it's still the highest one it will be the, the biggest month of the year. Finally, 8% more were sold in September than June. Well, let's see, September is 27 and June is 25. And, this is actually true because 2% of 2% of sorry, 8% of 25 is equal to two. So if we add two one to 25, we get 27. So, it is indeed 8%. That's all straightforward, hopefully. Let's now move on to the explore task. Okay, so now we're going to see an example of where we truncation can improve the scatter chart. So here, now, you can see below the data table was showing the height and age data that she's collected. And then in the chart, we have got the axes that have not been truncated, but have a think, how would you draw a version that you would, that would show the information better? Okay, great so if you decided that you would truncate both of these axes, then, really well done. And the reason that the reason why you might do this is because if you have a look at this data, it's actually quite hard to see what the relationship is. You can kind of see it as a positive correlation, but it's not really that easy to read off the different data. And you've got all of this black space down here that isn't really doing any much so you might as well truncate your axes as long as you are very clear about it. So, on the next slide, I will show you how you might do that. So yeah, here you've got some truncation and a computer programme I used it was difficult to do this that squiggle that we saw earlier so you could add back in if you're doing it by hand, but, as you can see, we have truncated the axes by starting the age at 10 and the height at 20, so we can see the data much more easily. The message of this lesson though, is however that you do need to be careful 'cause it may look for example, that this data point is significantly different from these data points. But actually, you know, the difference isn't as big as it looks because we have truncated the axes. That is actually it for today's lesson is been, you know, a bit of a short one. But it is an important one that you must remember to always check the, the values on your axes, the scale on your axes when you're comparing data. And when you're looking at axes in the real world, if you ever pick up a political leaflet, it's something to think about. So just have a think, are these politicians trying to deceive you? Now, you will be able to know if they are. That is it. Thanks very much for watching. See you next time. Have a great day, and bye.

In this lesson, we will discuss whether data in tables fit our hypotheses or not.

Data in tables

﻿Hello everyone it's Mr. Miller here. In this lesson, we're going to be looking at data in tables. So first of all, I hope that you're all doing well and only two lessons left of this unit to go. And over the last couple of lessons, we have been looking at scatter graphs, and we're going to take a break from that in this lesson by looking at data in tables, but we'll come back to scatter graphs for the final lesson of this unit. So without further ado, let's have a look at the try this task. Look at Binh and Zacki's statements below. Do you agree or disagree with them and why? And write your own similar statements. So have a read of what they're saying, have a look at the data from the table, write one or two sentences about what you think and pause the video now for two or three minutes so that you have time to do that. Okay. Great. So what Binh is saying is that since more people in year seven have no glasses, it proves that younger people have better eyesight. Well, although it's definitely true that 57 people in year seven have no glasses, which is more than the other years. We definitely can't say that they have better eyesight. And the main reason of course, is that you also need to have a look at the number of people that do have glasses. So it's not enough just to have a look at one piece of data. You have to look at, have a look at the whole table. Now, can you think of a way to, to test which which years of students need glasses the most or, or don't need glasses the most? Well, you could find the percentage of people in each year that have no glasses. So for example, in year seven, there are 102 students in total. So the percentage of people with no glasses is going to be 57 over 102, that turns out to be 56%. You can use a calculator for that. And in year eight, it's going to be 64%, and year nine, 57%. So actually it turns out that in year seven, there was actually the lowest percentage of people that don't need glasses. So this would appear that Binh's statement is, is, is not it's wider. The market is incorrect. But the other thing to think about here is what is the hypothesis? So she's saying that young people have better eyesight, but she's only looking at certain people in year seven, eight and nine. What about students who are even younger? Or what about students that are older? You just don't know. So the main message here is that you can't just look at these size of numbers. You have to look at numbers in proportion to each other, which sounds kind of obvious, but it's a really important one. And again, like we saw in the last lesson about truncating axes, this is all just making sure that you can interpret data in the best possible way. Let's move on out to the connect task. Okay. So for the connect slide, we've actually got the same table here. I just put into some total columns to make it a little bit easier. This time we have got four different questions. Let's have a look at the first one together. What percentage of year seven students wear glasses? So the first thing I'd recommend you do is find out all the totals. So this first one here is 102, and we can find out the other ones and that those totals are going to help us work out the answers. So the first question, the percentage of year seven students who wear glasses, well, I know that 45 years seven students wear glasses and there are 102 in total, so I can do 45 divided by 102, put that into a calculator, I get a 0.44 something. So I get 44%. That is the idea, pause the video now to have a go at the remaining questions. Great. Let's go through them. So first of all, completing the rest of the totals, well, I've got 56, I've got 90, 105, 143. And if I add up those totals in both the rows and the total row and the total columns, I'm going to get 248. And this tells me, what does this tell me this number? Well, this tells me the total number of all students, both with glasses, without glasses and in all three years. Anyway, let's walk through the questions here. So first of all, what percentage of students are in year seven? Well, first of all, how many students are in year seven? There's 102 hundred and 248 in total. So you just put that into your calculator and you get 41%. Next one. What percentage are in year eight and wear glasses? So you're looking at this 21 here over 248, and you put that into your calculator and you get 8% and I'm rounding these of course to the nearest percentage. Next one, which year group has the highest percentage of students with glasses. Well, you kind of do the same thing as we did in the previous slides, where we looked at the percentage with no glasses. So for year seven, you're going to look, you're going to do 45, over 102 which we've already done is 44%. And really the same for the other year groups. And we find that it's year seven, who have the highest percentage of students with glasses. Let's now move on to the independent task. Here's the table, and the table that I chose the favourite sport, played by some boys and girls in year eights discuss what data you would need to test the hypotheses below. And also it doesn't say here, but briefly comment on each of these hypotheses based on the data that you see. So three different statements to investigate, pause the video and spend four or five minutes on these questions. Okay, great. Let's go through it. So first of all, girls are more likely to prefer footballs to boys. Well, clearly we're going to have to look at the total number of boys and girls, who play football. So seven boys and ten girls, and just because there are more girls who prefer football than boys, it doesn't necessarily mean that girls are more likely to prefer football because we need to take into account of the total number of girls and the total number of boys. Of course. So the total number of boys is 20. Just adding up all the numbers in the boys row. Girls is 30. I think we take the percentages. So boys, it's seven over 20, which is the 5% prefer football in boys. And girls, it's 10 divided by thirty., which is 33%. We can see that actually boys are slightly higher. So we would say that this hypothesis, we wouldn't agree with this. Next one. Athletics is the most popular sport in the school. So hopefully what you said is this appears to be true because we've got 18 people in total, Who prefer athletics. Let's compare that to 17 people who, who, who like football. So it's not a, a huge difference, but you, you may think that athletics is the most popular sports by counting the total. Finally, swimming is the least popular sports. Well, if you look at the total for swimming is six and other is nine. So swimming is the lowest number, but does that necessarily mean it's that least popular sport? Well, it doesn't. And can you think whether it might be it's something to do with this group other. Well, of course, other sports that could be lots of different sports in that. So you could have cricket, which two people like and hockey, which one person likes and boxing, which two people like, and all those sports are less popular than swimming. So you definitely don't know for sure whether it's swimming is the least popular sport. Let's finally move on to the explore task. And here it is, we have got a nice table here, which shows grade in English versus grade in maths, three statements for you to have a look at this table is slightly different. So let's just make sure that we understand it. If we have a look at this two up here, well, that would mean that there are two people who got a seven in English and an eight in maths. So that should be quite straight forward. Pause the video. Now, read these statements and write down a sentence or two on each one, spend four or five minutes doing this, and then we'll discuss each one. Okay, let's come back together then. And hopefully you have written down something for all of these statements. The first one is something to catch you out. So although it does look like there's a line going down like that, which, you know, if we saw on a scatter diagram would mean a negative correlation. In this context, you have to be very careful. Because actually, if you have have a look at the scales, the, the higher up you go, the higher the mark in maths, but the further to the left you go, the higher your grade in English. So they're actually these guys, these students up here got a high mark in English and maths. And these students down here, Got a low in both. So actually the fact that we have this kind of line of best fit means that there is a positive correlation. So this first statement is definitely not true. Okay. What about the second statement? Students did better in math than they did in English. What do you think here? I'd be interested to know, and there's actually a number of things you could have done here. One thing is you could have just added up all the maths, all the marks in maths and added up all the grades in English. So for example, starting off in the top here in maths, that person got a nine. The next person here also got a nine in maths. This person here got a seven. We could have added up all the maths in mark, all the marks in math, sorry, and all the marks in English and compared them. And it turns out that maths, the maths total is slightly higher. So this statement could be true. You could have also found out the average mark in both. If you added them up first and then divided by how many students there are, That would have given you a similar result. And the final, 50% of students got above grade six in both subjects. Well, what did you think of this one? I think this is definitely false, we can have a look at all the students that got above six in both subjects. So we're looking for people that got at least seven in both, which are all of these people here, which is only one, two, three, four, five, six, seven, eight, nine students. And that is definitely not 50%. So we would definitely say that this last one is false as well. Okay. That is it for today's lesson. Thanks so much for watching. Hope you enjoyed it. Next time will be the final lesson. That's going to be a really interesting one, which will summarise a lot of the things that we have been looking at over this unit. So thanks so much for watching. Hope you have a great day and see you next time. Bye bye.

In this lesson, we will discuss which graph is the appropriate to display for a hypothesis.

Choosing the right graph

﻿Hello, everyone it's Mr. Millar here. In this lesson we're going to be looking at choosing the right graph. So first of all, I hope that you're all doing well and that you're ready for the final lesson in this unit. I hope it should be an interesting one where we're going to be pulling all the things that we've learned together into this unit. So without further ado, let's have a look at the try this task, and what's the same and what's different about these four graphs. We've got a couple of bar charts here, a pie chart, and a scatter graph. So write a sentence about what's the same, and what's different about these graphs. Pause the video now for a couple of minutes as to give yourself some time to do that. Okay, great, let's go for it. So, any number of things that you could have said, so we've already talked about the fact that, you know, we've got some bar charts, some pie charts and some scatter chart as well, but also you could put out the fact that in the first three charts, we're looking at favourite sports and actually these first two charts are showing the same data, but one is in a pie chart and one is in a bar chart. So you can see that in the bar chart, football is the largest and it's also the largest of the pie chart. And actually the same data is behind both of these bar charts. And in the third one here, well, that is very similar to the first one, but you've got two year groups, so you're comparing the data in the two year groups. And obviously the final one is a scatter graph, which we've been looking at a lot of this unit, so this is looking at something completely different, we're looking at some kind of test score and an exercise, and so this scatter graph, as we discussed lots of times, it allows us to look at the relationship between two pieces of data, and so we can look at the correlation, but in this case, there doesn't seem to be any correlation between the two, which sounds reasonable because we wouldn't expect to see a correlation between exercise and test score. Anyway, lots of things that you could have said here, let's have a look at the Connect slide where we're going to be diving into this in a bit more detail. So here's a Connect task and in this lesson, this is all about choosing the right graph. So in a moment, it's going to be up to you to decide which graph to choose, but now in this task, I just want you to think about looking at each of these four graphs, what data have to be collected for each graph to be made. So for example, in the first one, the only piece of data that you would have had to get is, what's your favourite sport? That is all, and then you simply had to count the number of people that said football and cricket, et cetera. So the first one, the data, as I said, is a favourite sports, it's up to you to have a think about the data, the variables that have to be collected for the other charts. Pause the video one or two minutes and write them down. Okay, let's go for it. So the one below that the pie chart, as I said before, it is a different type of chart, but showing the same data, and again, the only thing that you need to ask was favourite sports. And the comparative bar chart. Well, this is a little bit more detailed, isn't it? Because not only do you have to ask the favourite sport, but you also have to make sure that you know, what year the respondent is in, because you're comparing year seven to year eight. So you need to ask a favourite sport and what year group as well. So two pieces of data that you use to collect for the third one, and finally, what about the scatter graph? What two pieces of data do you need to collect for that? Well, it is nice and straight forward. You had to collect the test score and the number of times exercise per week. Now it's important to mention that when you're doing these surveys, there's lots of things that you could ask. So in the scatter graph, for example, you could be asking any other question as well, but the important part is that, in order for you to display the scatter graph, you must ask the test score and you must ask about exercise. So hope that was nice and straightforward for you. Let's now have a look at the independent task. Okay, so here's the independent task and it's a really important one, so make sure that you are ready. So throughout this unit, we've been looking at bivariate data which basically means comparing the relationship between data. And here in the table on the right hand side which is full of data, we've got some different countries, Belgium, France, Germany, et cetera, the continent that they're in, and the life expectancy and GDP. And just make sure you understand what these mean in case you haven't come across them before, a life expectancy is the number of years that someone would expect to live on average. So you can see that in the UK, for example, on average, when you're born today, a baby born today in the UK is expected to live for 81 years. And obviously you can see in other countries, it's a lot lower for a number of reasons. Maybe they have a worse healthcare system or whatever it is. And GDP well, GDP per capita means the amount of money earned per person per year on average. So for example, if you live in Germany, on average, you are making $46,000 per year, whereas someone in Ethiopia is only making 1,600. So that is what those two things mean. And let me explain what you have to do for this independent task. So what you have to do is, you have to complete this summary statistics for the following. So let's us do one example, let's do the first one, Western Europe sum life expectancy. So what does this mean? What sum life expectancy means, we need to work out the sum of all the life expectancies. And the reason that we need to do that is to work out the mean, and we know that to work out the mean we add up all the data and divide by how many there are. So we work out the sum overall, so we add together 81 plus 82 plus 81 plus 81, plus 83 plus 82 add them all together, you should use a calculator to do this, and you get a 490. That by itself is not very interesting, but what is interesting is finding the mean, so what you need to do is you need to look at how many pieces of data there are. So there are six countries in Western Europe, so you're going to have to do 490 divided by six, put that into a calculator and you get 82. So what that is saying is that the mean life expectancy at the average in Western Europe is 82, and looking at the data that seems to make sense. You also need to work out the range, so you know how to do that, you look at the biggest, which is 83, you take away the smallest from that, which is 81, so you get a range of two in Western Europe. Okay, so that is nice and straightforward. So a bit of working out for you to do, make sure that you have a calculator, and as you're working these things out, just have a look at the data and try to see what the data is telling you, because it's quite interesting. I took these from an official website, so it's quite interesting to look at the differences between the countries here. Pause the video and use a calculator to copy and to complete this whole table. Great, so well done for doing that, and here are the numbers that you should have. So there are the numbers for you, so we can see that on average, Western Europe has the highest life expectancy of 82 and also the highest GDP of over 39,000, whereas Africa, for example, has the lowest in both. So quite an interesting table. So that is the table that you need to have completed, so make sure that your answers are right. Let's move on now to the final slide of this here the Explore slide. Okay, so here is the question for you, which data would you display and in which graph to test the following hypothesis? So four hypotheses for us to do, let's walk through the first example. Western Europe has a higher average life expectancy than Africa or Asia. So you're thinking what data would you use and how would you display it and what type of graph to test this hypothesis. Now you're looking at average life expectancy, so clearly you would be thinking about a mean life expectancy for this one here. And you're looking for the mean life expectancy in Western Europe compared to Africa and compared to Asia. So you would need to look at those three pieces of data, mean life expectancy in Western Europe, in Africa and Asia, and second of all, what graph would you use to test it? Well, clearly a graph like a bar chart would work very well here, a bar chart would show you very clearly the results of that data. So that is all you need to do. First of all, the data that you would select, and second of all, the type of chart to display. Pause the video, and write down how you would display and in which graph the other three hypothesis. Okay, great, so let's go through these very quickly, so the second one, Asia has a wider spread of GDP per capita. Well, this one, because you're looking at spread of the data, you're looking for the range here, so you would compare the range of GDP per capita in Asia, compared to Western Europe compared to Africa, and you would display it again, probably in a bar chart. Next one, Western Europe has a higher average life expectancy and GDP per capita. Well, again, you would look to compare mean life expectancy and mean GDP per capita, and you would do this in a bar chart, but not just a single bar chart, a double bar chart or a comparative bar charts, so you might, for example, have, you know, for example, you could have these bars here could be the life expectancy for the three continents, and these three bars here could be the GDP per capita for the three continents. So you could have something that looked like that, something similar. And the final one, there's a positive correlation between life expectancy and GDP per capita. Well, hopefully you all said that you would look at some kind of a scatter graph here because you're looking at the correlation, you're looking at the relationship between these two variables. Let's have a look on the final slides at a couple of these graphs that you would get. So we just picked up a couple of here, first of all, the comparison of life expectancy with Western Europe, Africa, and Asia. So you can see nice and straightforward that Western Europe has the highest and Africa has the lowest. Notice that the scale in the graph here, I could have truncated it, I could have started at 50, I chose not to in this case, but that is an option. But yeah, this graph clearly shows that highest in Western Europe and lowest in Africa. Final one, a positive correlation between life expectancy and GDP per capita. Well, clearly you can see from the scatter graph that this hypothesis is definitely true. And I forgot to say that the first hypothesis also true, but yeah, you can definitely see the positive correlation, it looks a bit like a curve, so if I was drawing a line of best fit, it might look a little bit like that, but yeah, it's quite interesting, and it shouldn't surprise you that in countries where people are expected to live longer, there's also people are wealthy on average. And you could have a think about the correlation and the causation here, maybe it's the case that if people are richer then they live longer, maybe that's correlation in that way. It's really interesting that there's no, I don't have a definite answer for you, but it is definitely interesting to think about. So yeah, it's really important that when you're thinking about different hypotheses, you know what graph to use, that's been the main lesson for today, but in terms of the unit, that is everything. So I hope that you've enjoyed these lessons, really enjoyed talking to you through them. So hopefully you got something out of them, but anyway, I hope you good luck for the rest of your math scores in case I don't see you again and yeah, have a great day. Thanks so much for watching and bye.

Which of the following is the most appropriate line of best fit for the data?

The graph below shows the favourite sport of some pupils in Year 8, how many prefer boxing?

What variable(s) had to be collected for the chart below?

The scatter graph below shows the temperature and the number of ice creams sold at the beach on certain days. What was the temperature, in degrees, when 20 ice creams were sold?

Looking at the table below, what proportion of boys prefer sandwiches?

Unit Overview: Bivariate data

Lessons: