Lesson video

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.