Mr F’s Maths Notes

Statistics

5. Pie Charts

5. Pie Charts

Why do we bother with Statistical Diagrams?

• The answer to this question is similar to the one for: “why do we bother working out averages and measures of spread?”.

• We live in a world jam-packed full of statistics, and if we were forced to look at all the facts and figures in their raw, untreated form, not only would we probably not be able to make any sense out of them, but there is also a very good chance our heads would explode.

• Statistical Diagrams – if they are done properly - present those figures in a clear, concise, visually pleasing way, allowing us to make some sense out of the figures, summarise them, and compare them to other sets of data.

Big Example A group of 72 maths teachers were asked to choose their favourite TV show from a list, and their responses are shown in the table on the right. Construct a pie chart to illustrate this information

TV Show Total

Lost 12

Heroes 10

Desperate Housewives 4

Countdown 15

Teachers TV 13

The Beauty of Maths 18

1. Working out the Angles

• Before you can start to draw the pie chart, you need to know how big a slice each of the choices is going to take up – in other words, you need to know the angle of each segment

• To work this out, you need to remember that there are 360 degrees in a circle

• That means there are 360 degrees to share between each of the people who took part in the survey

• How many degrees does each person get?... Well, divide 360 by the number of people surveyed!To Calculate the Angles1. Add up the total number of pieces of data2. Divide 360 by this number – this tells you how many degrees is

allocated to each piece of data3. To work out the size of angle for each category, multiply the answer

to 2. by the number of people in each category – rounding your answers sensibly if you need to.

4. Check: Before you start to draw, make sure you check that your total number of degrees does add up to 360!

Our Example:

1. So, we have a total of 72 teachers who were surveyed.

2. 360 ÷ 72 = 5 So… each teacher is worth 5 degrees on our pie chart

3. We know how many teachers are in each segment, so let’s use our answer to 2. to work out what angle each segment gets

TV Show Total Working Out Angle of Segment

Lost 12 12 x 5 = 60 600

Heroes 10 10 x 5 = 50 500

Desperate Housewives 4 4 x 5 = 20 200

Countdown 15 15 x 5 = 75 750

Teachers TV 13 13 x 5 = 65 650

The Beauty of Maths 18 18 x 5 = 90 900

Remember: Check this column adds up to 360 before you move on!

2. Drawing the Pie ChartYou’ve done all the hard work, and drawing the pie chart should be easy… but you’ll be amazed how many people mess it up, so take your time and follow these steps…

1. Draw a circle using a compass. Mark the centre with a dot and draw a straight line from the centre up to the right of your circle

2. Carefully place your angle measurer along the line, with the centre exactly on the centre of the circle. Now, count around from 0 until you reach the correct number of degrees – in this case 600 – and place a dot

Lost

3. Join up your dot to the centre with a straight line, and label your segment.

4. Now, this is the tricky bit… turn your pie chart clockwise until your new line is horizontal (where the first line used to be). Now you can mark your next angle in exactly the same way.

LostLost

5. Keep doing this until you have drawn all your segments

6. If you want to you can colour in your segments, but you must remember to label them clearly, or add a key!

Check: You will know if you have got it right if the line to make your final segment is the very first line you drew!

Maths Teachers' Favourite TV Shows

Lost

Heroes

DesperateHousewives

Countdown

Teachers TV

The Beauty ofMaths

3. What CAN we tell from Pie Charts

• Well, if you look back at our pie chart, you will see that it shows pretty clearly that The Beauty of Maths was the most popular choice amongst our maths teachers, whereas Desperate Housewives was the least popular

• If you want to be really fancy, you might be able to say things like: “roughly 3 times as many teachers preferred Lost to Desperate Housewives”

4. What CAN’T we tell from Pie Charts

• Well, imagine we were just given our pie chart (and no original data), and someone said: “how many maths teachers said that Countdown was their favourite show?”, what would we say?...

• Well, probably not a lot, because there is no way of knowing!

• Unless we are told how many people were surveyed all together, we cannot answer that question!

• When making statements based on Pie Charts, just make sure what you are saying is definitely, 100% true!

5. Interpreting Pie Charts

Big Example 2 240 Maths teachers were asked “what is your favourite drink?” and a pie chart was drawn to show to information.Work out how many teachers preferred coffee

TeaCoffee

J20

Squash

Milk

Water

108o

84o

60o

48o 36o

24o

To answer this question we must do the opposite of what we did when we were drawing the pie chart – we must use our angles to find our totals!

Let’s look at coffee… it takes up 840 out of 3600, and what we want to know is “how much does it take up out of our 240 people?”

Well, what about using this as an excuse to show off our Algebra skills!...

84

360 0

?

24 Multiply both sides by

24084

240 360

?

So, turning to our calculator, we get an answer of… 56 people

Good luck with your revision!