Smoking causes lung cancer. What kind of correlation would you expect to see?

There is a positive correlation between the number of pets people own, and the number of books people read. Which of these statements is most likely to be true?

What correlation would you expect to see between the variables weekly salary and amount spent on food per week?

Which of the following statements is most likely to be true?

Bivariate Data Lesson 5:

﻿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.

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:

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

Maths

Y8 Maths

Key Stage 3

Year 8

Truncating axes

Bivariate data

Statistics and probability

THEME

UNIT

Univariate and bivariate data

Representing bivariate data

Correlation

Lines of best fit

Correlation and Causation

Data in tables

Choosing the right graph

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

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

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:Truncating axes

Core Content

Bivariate data: