Transcript Pie Charts - Chiltern Edge School

Mr Barton’s Maths Notes
Stats and Probability
5. Pie Charts
www.mrbartonmaths.com
5. Pie Charts
• The answer to this question is similar to the one for: “why do we bother working out averages
Why do we bother with Statistical Diagrams?
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 Angles
1. Add up the total number of pieces of data
2. Divide 360 by this number – this tells you how many degrees is allocated to
each piece of data
3. 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 Chart
You’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
3. Join up your dot to the centre with a straight line,
and label your segment.
Lost
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.
5. Keep doing this until you have drawn all your segments
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!
6. If you want to you can colour in your segments, but you must remember
to label them clearly, or add a key!
Maths Teachers' Favourite TV Shows
Lost
Heroes
Desperate
Housewives
Countdown
Teachers TV
The Beauty of
Maths
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
Coffee
Tea
o
84o 108
24o
o
Milk
60
o
o 36
48
J20
Water
Squash
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

?
Multiply both sides by 240
24 0
So, turning to our calculator, we get an answer of… 56 people
84
360
 240  ?
Good luck with
your revision!