Lesson video

Hello, my name is Dr.

Rowlandson, and I'm excited to be guiding you through today's lesson.

Let's get started.

Welcome to today's lesson from the unit of graphical representations of data.

This lesson is called Problem Solving with graphical representations of data, and during our lesson we'll be using our understanding of various graphical representations in order to solve problems. Here's a reminder of some keywords that you may be familiar with and can help us during today's lesson.

This lesson contains two learning cycles with the first learning cycle, focusing on solving problems with many different types of graphical representations of data.

We often see bar charts, pie charts, and scatter graphs when we're handling data.

That's because these are common ways to represent data visually.

However, these are not the only types of graphs.

Graphs and charts come in many different shapes and sizes.

Therefore, data can sometimes be presented using variations of these common graphs or in other unusual ways.

One problem that it creates is it makes it difficult to learn about every single type of possible graph that we might see, because there are so many graphs out there, and even the ones that we are used to can be altered and changed in a way to represent something different about the data and also new graphs are being invented regularly.

Therefore, an important skill for solving problems with data is to be able to interpret data when it's presented to us in novel ways.

The good news is that a whole point of presenting data in a graph or a chart, is to make something as clear to see as possible.

Here's an example.

The graph shows data about the population of Benin in 2016.

This graph is called a population pyramid, and it looks a little bit like a bar chart except unlike the usual bar charts we see, the bars are going horizontally.

They're going back-to-back away from each other as well.

When we look at this population pyramid, we can see that there's a vertical axis going up the centre of it, with age groups, for example, zero to four, five to nine, those are the age groups of the population.

And then along the horizontal axis, we have the population in thousands there too.

On the left, we have bars representing the male population of Benin, and on the right, we have the female population.

So, for example, the bar on the bottom left-hand corner, shows us that there are 880,000 people approximately in Benin who are males between the age of zero and four years old.

Let's use this graph now to determine whether some statements are true or false based on the data we can see.

The first statement is: there are more men than women.

Let's take a look at the graph.

It looks fairly symmetrical on both the male and the female side, implying that roughly, there are about the similar number of males and females in this population.

We don't know for sure, but it looks roughly like it, they are approximately similar.

So that one would say would be false based on this data.

The next statement says the biggest population group is babies and toddlers.

Let's take a look at the vertical axis and go down to ages what we'd consider to be babies and toddlers.

That would be around about zero to four years old.

We can see that both on the male and female sides of this population pyramid, the bars for babies and toddlers for zero to four, are longer than all the other bars, so we'd say that this statement will be true.

The biggest population group does appear to be babies and toddlers.

The next statement says, there are not many elderly people.

Let's look at the top end of this population pyramid, where the oldest members of the population are.

We can see the bars at the very, very top are the smallest bars in this graph.

Therefore, that would suggest that this statement is correct compared to the rest of the population, there are not many elderly people.

And the last statement is, the biggest population group is working-age men.

So there's two things we need to look at here.

We need to look first at the male side of the population pyramid and compare it to the female side, and also we need to look around the middle of the age groups as well, because those tend to be working-age people.

However, in this case, we can see that there are a lot more people who are between zero and four years old and then five and nine years old, and then 10 and 14 year olds.

Actually, as we get older, they seem to be fewer and fewer people in this population.

Therefore, that would suggest that the biggest population group is not working-age people, let alone working-age men, so that would be false.

Let's check how well we've understood that idea.

The graph shows data about the population of Qatar in 2016, and again, it's a population pyramid with males on the left, females on the right, and ages going up the centre of that graph.

Which statement is true about Qatar in 2016's data? A, there were more men than women.

B, there were more women than men.

And C, there were approximately the same number of men and women.

Pause the video, choose which one you think is true, and press Play when you're ready to do it together.

The answer to this one is A, there were more men than women in Qatar in 2016.

We can see that on the graph, because the bars for the male side of the population pyramid are much longer than bars on the female side, suggesting that there was a greater number in the population of male people than there were in female people in Qatar in 2016.

Here's another question based on the same graph: Which is the biggest population group in this data.

Is it A, babies and toddlers? B, working-age men, or C, elderly women? Pause the video, make a choice, and press Play when you're ready for an answer.

The answer to this question is, B, working-age men.

We can see that, because there is quite a large bulge in the data on the male side of the graph between the age of 20 and 50 years old.

That would suggest that there are more working-age males in Qatar than any other population group in that year.

While the previous graph looked a little bit like a modified bar chart, some graphs look completely different altogether.

For example, the graph here shows data from the Met Office about average rainfall in millimetres per month in Aberporth, from 1941 to 2022.

This graph is sometimes called a radar chart, and the way it works is we have a circle, and around the outside of the circle we can see the months of the year.

And the months of the year are in a cycle.

We go from January to December, then to January again, and so on like that.

And then we can see from the centre of the graph there is a straight line going out to each of the months.

These straight lines are a bit like an axis, and we can see that there are numbers going along the vertical straight line from the centre to January, the numbers 25, 50, 75, 100 and 125.

The smallest circle around the centre has the 25 on it.

Therefore, any points plotted on that circle line represent 25 millimetres of rain, and as we go further out of the graph, it represents more and more rain.

We can also finally see a purple squiggly line around the radar graph of some kind.

Those are points that have been plotted on each of the months and then joined up afterwards.

So, let's use this graph now to solve some problems. Which month tends to be the wettest? Let's look at the plotted points on the radar graph and see which one appears to be the furthest out from the centre.

In this case, it is November.

Which month tends to be the driest.

Again, we can look at the points that have been plotted on the radar chart and look which point is the closest to the centre.

It looks like it is April.

And which month tends to be wetter, February or August? If we take a look at February first, we can see that the point is somewhere between two rings.

One ring is labelled with 50, and the other ring is labelled with 75.

Therefore, we don't know precisely what the rainfall was in February, but we know it's somewhere between 50 and 75.

Let's now look at August.

The point for August is pretty much on the ring, which is labelled as 75.

So February has somewhere between 50 and 75 millimetres of rain.

August has 75, or pretty much close to 75, therefore the wettest month tends to be August.

Now, we can present the same data using multiple different representations.

For example here, the bar chart and the radar graph both show the average rainfall.

It's the same data, just presented differently.

However, using multiple representations for the same data, is not always necessary, and it can sometimes be a bit distracting to have lots of different graphs shown the same thing, because it means the reader doesn't necessarily know what to focus on.

Therefore, it may be better to choose a graph that presents what you want people to see about the data in the clearest possible way.

That means there's no one type of graph, which is always better than another type of graph.

It really depends on what it is we wanna try and get across.

So what could be the advantages of using each of these different types of charts? What might be the advantage of displaying this data in a bar chart rather than a radar graph? And what might be the advantage of displaying this data in a radar graph rather than a bar chart? Pause the video, have a think, and press Play when you're ready to discuss this together.

Let's take a look at this.

One advantage of a bar chart is that it's easier to compare one month than another, than it is with a radar graph.

That's because you can take a month like January, put a ruler on top of the bar and look across the ruler to see which bars are higher and which bars are lower.

It makes that month-to-month comparison easier.

One advantage of displaying this data in a radar graph could be that it shows the year as a cycle by linking up December and January, because that's what a year is, it's a cycle.

And the weather data for December will be quite similar to the weather data for January, because those are adjacent months, which we don't see quite so clearly on a bar chart.

Okay, let's check what we've learned with that.

Based on the data in this graph, which month tends to be the wettest? Pause the video, write down one of the months, and press Play when you're ready for the answer.

The answer is October.

We can see, because the point for October is the furthest out from the centre on this graph.

Based on this data, which month tends to be the driest? Pause the video, write down a month, and press Play when you're ready for an answer, The answer is, May.

We can see that, because the point for May is the closest to the centre out of all the months.

Time for some practise now with Task A.

This task contains two questions.

Question One has a population pyramid, this time for Japan in 2016.

There are four statements written about this graph.

You need to read the statements, take a look at the graph, and then decide which of those statements is true.

Pause the video, have a go, and press Play when you're ready for Question Two.

Here is Question Two.

We have another radar graph from the Met Office about the average rainfall.

However, this time it is for two towns.

We have a bold, purple line representing data for Eastbourne from 1941 to 2022, and we have a dashed teal line to represent Stornoway.

There are three questions.

Read each question, look at the graph and write down your answers.

Pause the video, have a go, and press Play when you're ready for answers.

Well done with that.

Here are the answers now for Question One.

We need to tick the statements which are true based on the data represented in the graph.

The first true statement is that there are not many people over 90 years old.

We can see it on the graph because 90 and above, those bars are the smallest bars of that population.

And the other true statement was that the number of babies born has gone down over time.

That one's a little bit more subtle, but the way we can see that is, if we look at the bars, for example, around 65 to 69 years old, those bars are the longest, which means 65 years ago, there were a lot of babies born.

And as we go down the vertical axis, and look at, particularly, the bottom 30 years, we can see those bars are getting smaller, and smaller, and smaller.

Therefore, the number of babies born of those times, has gone down over time.

And here is Question Two, which town tends to get the most rainfall? That is Stornoway.

We can see that because the dashed line is further out than the bold line at all points.

Which town tends to have its wettest month in November? That is Eastbourne.

And we can see that, because if we just look at the bold line, we can see the bold line is the furthest out from the centre in the month of November, whereas that's not the case with the dashed line.

With the dashed line, it looks more like it's December.

And C says, which tends to be wetter: Eastbourne in February, or Stornoway in July.

Let's take a look at Eastbourne in February first.

We can see the point for February for the bold line is just above 50, and if we look then in July and the dashed line, it is pretty much on 75, therefore, it means Stornoway must get more rain.

So, it's Stornoway in July.

Great work so far.

We're now onto the second learning cycle, which looks at responding to additional data.

Here we have, Jacob, and Jacob claims that summers tend to be getting wetter every year.

So, to investigate his claim, he presents rainfall data for each August in Bradford from 1998 to 2002.

Jacob has made a few choices here when it comes to which data to collect.

He's chosen to focus on a particular city, so he's comparing data from Bradford at one point at a time to Bradford at another point at a time.

We've got an assumption here that we'd expect the amount of rainfall to be similar in Bradford for different years, because it's the same place.

He's also chosen a particular month to focus on.

He's chosen August and to look at data points for August each year.

This is probably a better comparison to make than looking at different months within the same year, because you would expect the amount of rainfall to change from May to June, to July to August or September, really depending on the seasons.

Therefore, by choosing the same month of each year, you would expect August of one year to have a similar amount of rainfall to August in another year, particularly in the same city.

Looking at this graph, we can see that the line appears to be going up.

It's at its lowest in August, 1998.

It's at its highest in August, 2022, and it's going up each year.

Therefore, the graph appears to support his claim.

However, we could suggest that there are some problems with this claim based on the data that Jacob is presenting.

Why might this data not fully support Jacob's claim? And how could he be more sure about his claim? Pause the video, have a think about these questions, and press Play when you're ready to discuss them together.

One reason why this data might not fully support Jacob's claim, is that the graph only shows five years of data here, it only shows from 1998 to 2002.

We don't know what the data does after 2002, whether not it continues to increase, and what was the data doing before 1998? Was it increasing then as well? We've only got a small snapshot of five years here.

How could he be more sure about his claim? Well, he could collect more data, and see if that trend is continuing over a longer period of time.

So Jacob investigates his claim further by collecting rainfall data for the next four years.

Let's plot this data on the graph.

We got here, in 2003, there were 9.

6 millimetres of rain.

In 2004, there was 189.

9 millimetres of rain.

In 2005, there was 47.

5 millimetres of rain, and in 2006, there was 92.

7 millimetres of rain.

Now, we've plotted those points, let's join them up with a line.

Hmm.

How might this additional data affect Jacob's claim that summers are getting wetter every year? Pause the video, have a think, and press Play when you're ready to continue.

It shows that the amount of rainfall in August has increased and decreased multiple times between 1998 and 2006, meaning that it's not got wetter every year, like in Jacob's claim.

When we plot even more data all the way up to 2022, we can see that it's going up and down all the time.

There are some consecutive years where the amount of rainfall does increase every year.

However, there are also some consecutive years where the amount of rainfall decreases each year.

For example, in this case, we can see it's gone down each time in that box there.

Therefore, when we only look at a small amount of data, it can give a false impression.

In Jacob's case, he looked only at the data from 1998 to 2002, and in that situation, that small window, the data was increasing each year.

In the box that's highlighted now, if we only look at that data, it looks like it's getting drier every year, so we should be careful not to make claims based on small amounts of data, 'cause these small snapshots can sometimes be quite misleading.

And, remember, that a fuller picture may be obtained by considering more data.

We could even argue that this graph still does not contain enough years to give us a good sense of what's going on.

If we had data for say 100 years, then yes, we may see the amount of rainfall going up and down every year, but overall, the points may be generally moving it in one direction or another over time.

Okay, let's check what we've learned with that.

True or false? A small amount of data is enough to be certain about a claim.

Decide true or false, and choose one of the justifications below: A, the data is enough to show that the claim is definitively correct, and B, including more data might give a different impression.

Pause the video, make your choices, and press Play when you're ready for an answer.

The answer is false, because including more data, might give a different impression.

Here's another situation.

Sam investigates which genre of books is more popular: fiction or nonfiction.

They do this by asking five people whether they prefer reading fiction or nonfiction, and then presents the data in a bar chart.

Sam concludes, based on the bar chart, that fiction is a more popular genre than nonfiction.

What could Sam do to be more confident about their conclusion? Pause the video, write something down, and press Play when you're ready for an answer.

One thing that Sam could do, could be to ask more people.

It might be that if Sam asked two more people, they might happen to both like nonfiction, and then that would be the tallest bar.

If Sam asked 100 people, then they might be more confident about the conclusions than they are with just five people.

Over to you now, for Task B, this task contains one question.

In this question, Sofia investigates whether there is a connection between sunshine and temperature.

She collects weather data in Bradford for each March from 2017 to 2022 and plots a scatter graph.

She concludes that there is no connection between the variables, and we can see why that's the case.

We've got five of those points, all seem to be this similar height, but for different amounts of sunshine.

So here's where you come in: Part A, the table shows additional data from 2012 to 2016.

Plot these points on a scatter graph, and then Part B, decide how might these additional points affect Sofia's conclusion.

Pause the video, have a go, and press Play when you're ready for answers.

Well done with that.

Here are the answers: In Part A, we need to plot the additional points on the scatter graph.

This is what it should look like once those points are plotted.

And then Part B, it says, how might these additional points affect Sofia's conclusion? Before we plotted these additional points, most of the old points were all a similar height, but for different durations of sunshine.

Now we've plotted these new ones, we can see there's a bit more of a clear upward trend, a bit more of a shape going diagonally up the scatter graph.

Therefore, it looks more likely that there could be a connection between the variables.

It looks more likely that the more sunshine there is, the greater the mean of the daily maximum temperature is.

Therefore, months with more sunshine tend to have higher temperatures.

However, more data could make it even clearer whether or not there is a connection.

Fantastic work today.

Here's a summary of what we've learned in this lesson.

Firstly, we've learned that data can be presented in various different formats.

Graphs and charts come in all sorts of shapes and sizes.

However, we've learned that representing the same data in multiple different ways, may not always be necessary.

And we've learned that small amounts of data on a graph can sometimes be misleading.

Therefore, a fuller picture can be obtained when we consider more data.

Well done.