Sector Graphs
Pie Charts are also called Sector Graphs because the pieces of pie' are mathematically referred to as sectors. The total circle represents all the scores in a data set. Each sector in the circle is proportional to it's corresponding category's percentage of the whole data set.
Constructing a Pie Chart (or Sector Graph)
Remember there are $360^\circ$360° in a circle. So our whole data set needs to take up $360^\circ$360° and we need to make sure there are no gaps between the sectors.
Each group in our data set will be represented by a different sector in our graph. We calculate the size of each sector by multiplying $360^\circ$360° by the fraction or percentage each category represents of the whole data set.
Example
Question 1
Let's say we ask $50$50 people to choose their favourite colour. $18$18 people said red, $20$20 said blue and $12$12 said yellow. Let's look at how we would construct a sector graph to display this information.
The first thing we need to do is express the number of people who like each colour as a fraction of the whole sample:
Red: $\frac{18}{50}\times360=129.6^\circ$1850×360=129.6°
Blue: $\frac{20}{50}\times360=144^\circ$2050×360=144°
Yellow: $\frac{12}{50}\times360=86.4^\circ$1250×360=86.4°
We can check we've calculated everything correctly by adding up our answers:
$129.6+144+86.4=360$129.6+144+86.4=360 - awesome!
Interpreting a Pie Chart (or Sector Graph)
Instead of working out the size of the angles from our data set, we work in reverse to find how many units the sectors in our graph represent.
Example
Question 2
Let's say that a store stocked four brands of DVD players and they recorded the number of sales of each brand in a sector graph, shown below:
As long as we know the total number of sales, we can work out how many of each brand were sold.
If the company sold $1500$1500 DVD players in total, how many Brand B DVD players were sold?
We can see from the graph that Brand B makes up $90^\circ$90° of the sector graph. $90^\circ$90° is the same as $\frac{1}{4}$14 or a quarter turn. How many DVD units do this fraction represent?
| $\frac{90}{360}\times1500$90360×1500 | $=$= | $375$375 dvd players |
Worked Examples
Question 3
Some non-profit organisations were asked how many operations they are running. The results are given below:
| Number of operations | Number of non-profit organisations |
|---|---|
| $10$10 | $4$4 |
| $15$15 | $11$11 |
| $20$20 | $45$45 |
Consider a sector graph of this data, where each sector represents the number of organisations which have $10$10, $15$15 or $20$20 operations.
What is the angle of the sector representing the organisations with $20$20 operations?
QUESTION 4
The sector graph represents the number of people taking leave from work at a particular company.
If $5$5 people took leave in January, how many degrees represent $1$1 person?
How many people took leave in November?
How many people took leave between the beginning of November and the end of March?
What percentage of the people took leave in December?
Give your answer as a percentage, rounding to two decimal places.