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

Looking at the same graph, is the following statement true or false: "Triple the number of people prefer boxing to athletics"

Which statement is true? Select one.

Bivariate Data Lesson 6:

﻿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.

Now it is time to test our learning with a quiz.  Good luck!

Look at the table below, which shows the favourite lunch option for boys and girls in Year 8. First, how many boys in total were asked?

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

Looking at the table again, which of these statements is INCORRECT?

Data in tables

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

Maths

Y8 Maths

Key Stage 3

Year 8

Bivariate data

Statistics and probability

THEME

UNIT

Univariate and bivariate data

Representing bivariate data

Correlation

Lines of best fit

Correlation and Causation

Truncating axes

Choosing the right graph

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

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?

Lesson overview:Data in tables

Bivariate data: