Lesson video

Good day everyone.

Thank you for joining me for today's maths lesson.

I'm Mr. Gratton, and today we will be considering different statistical representations and the insight that they may give to a data set.

For most of this lesson, we'll be focusing on pie charts and bar charts.

Pause here to familiarise yourself with the definitions of these charts.

To start, let's compare some pie charts and bar charts.

Both bar charts and pie charts are used to visually represent data that has been collected.

When looking at these charts briefly, at a quick glance that is, they can both show key insights to this dataset.

Which insights are more easily understood from this quick snapshot look at each of the charts? The bar chart and the pie chart.

Well, a quick look at a bar chart can help compare between each subgroup of data.

For example, it rained on more days than it was dry.

A quick look at a pie chart can help compare one subgroup against the whole dataset.

For example, it rained on a majority of the days last month.

We can describe these comparisons in more detail.

By reading the heights of the bars, rained occurred roughly three times as often as it was dry.

From looking at the pie chart, dry looks just over 90 degrees, a quarter of the whole dataset.

Looking at the modal activity, which is the activity that occurs most frequently, you can see that the most frequent activity is sports.

Both by quickly looking at the pie chart, sports has the biggest sector.

And the bar chart, sports has the tallest bar.

On the other hand, finding out how frequent sports was.

Well, we can read this quite easily on the bar chart by looking at the height of the bar.

From the height of this bar, we can see that sports occurs 18 times, but a pie chart cannot tell you any frequencies without any further information being provided.

But to a pie charts benefit, we can more easily tell that board games appears a quarter of the time, a quarter of the total frequency of the data collected.

This can be seen on the pie chart because a quarter is represented by that 90 degree right-angled sector.

We can also figure this information out on a bar chart, but that would require quite a few calculations and so is a much slower process than the easy spot with the pie chart.

And finally, if looking to find how many more students did homework versus film club, we can read the frequencies of homework and film on the bar chart and then do a subtraction.

But again, because this question talks about frequencies, the pie chart really isn't useful.

If a frequency for one sector was given or the total frequency that the pie chart represents was given, it would be possible using proportional reasoning.

But this would again take much longer than simply using the bar chart and one simple subtraction between the heights of two bars.

Here's a quick check.

Which of these questions can be quickly answered using this bar chart? Pause here to consider each question.

A and D can be answered quickly as these questions require you to look at a frequency.

Similar again for this pie chart, which of these questions can be easily answered? Pause here to consider each of these four questions.

The answers are B and C as these questions check for a proportion rather than frequency.

Okay, but what about bar charts and pie charts that have many more subgroups? In the case of months, 12 subgroups, one for each month.

For bar charts, it is still quite easy to gain that insight.

November is clearly the modal month 'cause it has the highest bar.

It is easy to read that February has a frequency or a height of 24 on a bar chart, and we can see that the lowest height is June, and so that is the least frequent birth month.

However, for a pie chart, it may lose some of its benefits.

You can tell November is the modal month, but it isn't very clear and it's definitely not as clear as the bar chart.

But even though proportion is the specialty of a pie chart, it is quite hard to tell if any month had more than 10% of the students representing it.

We can find this information out using a protractor, but we certainly cannot do it by looking at a quick snapshot at this pie chart.

It is also tricky to interpret anything for low frequency sectors.

Notably when there are a handful of sectors that are all low frequency, meaning they all have small angled sectors on the pie chart that are tricky to distinguish by sight.

Furthermore, it is highly impractical and impossible without a protractor to calculate any frequencies as you would need further information and use proportional reasoning calculations to find these frequencies out.

Finding out the number of people born in October cannot be done at a quick glance and it would require far more calculations than using a bar chart.

To the defence of pie charts, broader insights can still be possible.

We know that more than 25% of students were born in these winter months of November, December, and January.

I personally think it is much quicker and easier to spot this type of information from a pie chart compared to the same question on a bar chart.

Is it pretty obvious to you that November, December and January using a bar chart represents 25% of the data? It's not as obvious.

So for data sets with many subgroups, bar charts retain its specialty in reading frequencies, but to gain insight into proportion, you would have to add up all of the heights of all of the bars to find the total frequency first.

Pie charts retain some of its specialty in reading proportion, but you would either need a protractor or at least one frequency to gain any further detailed insight using a pie chart.

Okay, two quick checks.

First one, from only a quick glance at the pie chart and bar chart, which mode of transport was most frequently used and which graph (or both) is it possible to answer part A.

Pause to check both of these charts.

The answer is bus.

And it was possible to tell this from both charts because bus had the largest sector and was the tallest bar on the bar chart.

Similar question again, did more, less, or equal to 25% of students walk to school and with which graphs could you answer that question? Pause to give this a go.

The answer is more than, and it is much clearer to answer that using the pie chart than the bar chart.

This is because we can see that the walk sector had a sector size greater than 90 degrees.

Whilst tricky to calculate, it is still possible to find this information from a bar chart, just not with a quick glance at the two charts.

Time for some practise.

Put a tick by the statements that were easily gathered using this pie chart.

Pause to look through all five of these sentences.

For question number two, for each of these five questions, put an answer in the pie chart column or the bar chart column or both.

Pause now to do this for parts A, B, C and then pause again for D and E.

So pause now to answer questions A, B, and C.

And again for questions D and E.

For question number three, for each of these questions, write down a "Q" if the question can be answered quickly by a quick glance, write down an "S" if you can answer that question after one single calculation, such as a subtraction, or "M" if you need many calculations in order to answer that question.

Afterwards, if you can, then answer each question.

Pause to give yourself some time to do this.

Onto the answers.

B, D and E were possible to gather from this pie chart.

And for question number two, the mode of raincoat can be easily gathered from both the pie chart and the bar chart.

For parts B and C, however, you can only easily gain this information from the pie chart.

However, it is still possible to do from the bar chart if you spent time doing the calculations.

For parts D and E, the frequency answers are both found using the bar chart.

And for question number three, here are the answers.

Pause here to check your answers against the ones on screen.

For this cycle, we'll be looking at a completed chart and comparing it to an incomplete chart of the same data in order to attempt to complete it.

Such as here, this pie chart is complete but the bar chart is incomplete.

We can use a protractor to measure the angles on the pie chart and use this information to complete the bar chart.

Notice how coffee is half the angle of water.

This means that coffee on the bar chart will be half the height of water.

And so as we can see, the height of water was six and so the height of the coffee bar must be three.

The same applies for juice being half the height of tea.

If tea had a height of 10, then juice must have a height of five.

Here's a check, which two drinks were equally frequent? Pause here to find which chart says this information clearly.

The answers are water and juice.

They both have the same frequency as seen by them both having a 90 degree sector on the pie chart.

Using this information, what should the height on the bar chart be for water? Pause to make the link across these two charts.

The answer is nine squares.

The same as the height for juice.

Here are the angles for milkshake and fizzy.

How tall should the bar for milkshake be? Pause to make the comparisons using these angles.

The answer is 12 squares.

This is because milkshake was double the angle of fizzy and so the bar must also be double in height.

Onto some practise questions.

Complete the bar chart using the information in this pie chart.

Pause to take in all of this information.

Question number two is similar to question one, but this time you'll need to use a protractor to measure the angles in the pie chart for yourself.

Pause to find the angles in this pie chart and then complete the bar chart.

Question three is the other way around.

The bar chart is complete this time, but the pie chart is incomplete.

Pause to find the total frequency of the bar chart and use this information to complete the pie chart.

Here are the answers.

Five times the number of people voted for dinner than lunch.

Therefore the bar should be five times as tall, giving you a total height of 10 compared to two for lunch.

For question number two, first of all, here are the angles.

Any angle measured to within around two degrees of the ones that you see on screen is completely fine.

Pasta should be the same height as sandwich at a height of six whilst snack should be one third the height of roast dinner at three rather than the nine of roast dinner on screen.

For question three, here are the angles for the three sectors of this pie chart.

In today's lesson, we have compared both pie charts and bar charts and used one to complete the other.

Very, very good work in today's lesson.

Thank you so much for joining me, Mr. Gratton, and I hope to see you soon for some more maths.

Have a great day.