Construct Pie Charts

Do you like pies?

 

 

Today we'll be looking at how to construct pie charts.

(Though unfortunately we won't be able to eat them!)

 

A pie chart is a circular chart that is divided into slices (just like a pie!).

 

It looks like this:

 

 

For example, here we can see that each slice represents a subject and art has the biggest slice - that means it was the most common data point!

 

Let's see how we would construct a pie chart of our own:

 

Year 7 was surveyed to find out their favourite lunch choices.

 

The results were organised into a frequency table:

 

Lunch Choice	Frequency
Pizza	12
Sandwiches	8
Pasta	6
Salad	4

 

 

Now how do we make this into a pie chart?!

 

Well, we know all of the pie chart needs to represent all of the responses.

Altogether, we had 12 + 8 + 6 + 4 = 30 responses.

We can see that we got this by adding all the frequencies together.

 

We know the full turn angle of a circle is 360°.

That means 360° will need to represent the 30 students.

 

So we can write:

360° = 30 students

 

Dividing both of these figures by 30, we find that:

12° = 1 student

That means each student will occupy 12° of the pie chart!

 

Lunch Choice	Frequency
Pizza	12
Sandwiches	8
Pasta	6
Salad	4

 

Looking back at the frequency table, we can see that sandwiches for example, has the frequency of 8.

This means that 8 students chose sandwiches.

So, these students' slice in the pie chart will have the angle of 8 x 12° = 96°

(We call this the central angle for the response of sandwiches.)

 

We just multiplied the frequency with how many degrees correspond to 1 response! 

Easy!

 

We can then find the other central angles in the same way and organise it neatly in the table by adding an extra column:

 

Lunch Choice	Frequency	Central Angle
Pizza	12	12 x 12° = 144°
Sandwiches	8	8 x 12° = 96°
Pasta	6	$\frac{}{}$6 x 12° $\frac{\mathrm{}}{}$°
Salad	4	$\frac{}{}$4 x 12° $\frac{\mathrm{}}{}$°

 

We would then use our protractors to construct all the angles and so the pie chart!

 

 

Let's have a go at some questions!