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Primary - Stage 3 (Year 5 & 6) Stage 3 (Year 5 & 6) Data

Interpret sector (pie) graphs

20 practice questions 0 video lessons Theory + worked examples
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Theory

A sector graph shows a whole group as a circle cut into sectors, so each sector is the fraction of the whole its category takes. Multiply a sector's fraction by the total to find how many it stands for.

A sector graph (or pie graph) shows a whole group as a circle cut into sectors, one for each category.

The whole circle stands for the whole group, so all the sectors together make one whole.

A bigger sector is a bigger fraction and a larger part of the group.

To find how many a sector stands for, multiply its fraction by the total: \(\text{fraction}\times\text{total}\).

Sector graph of favourite drinks A circle divided into three sectors. Water fills one half, Juice fills one third and Milk fills one sixth. The whole circle stands for 24 students. Water1/2 Juice1/3 Milk1/6
The circle is \(24\) students. Water is half, so \(\dfrac{1}{2}\times 24 = 12\); Juice a third gives \(8\); Milk a sixth gives \(4\). The three add to \(24\).

Each sector can be read as a fraction and as a number.

DrinkFractionCount (of 24)
Water\(\dfrac{1}{2}\)\(12\)
Juice\(\dfrac{1}{3}\)\(8\)
Milk\(\dfrac{1}{6}\)\(4\)
The fractions add to one whole. \(\dfrac{3}{6}+\dfrac{2}{6}+\dfrac{1}{6}=1\), and the counts \(12+8+4=24\).

How to read a sector graph

  1. Compare the sectors to see which fills the most of the circle.
  2. Name each sector's fraction of the whole.
  3. Multiply a fraction by the total to find how many it stands for.
  4. Check that the fractions add to one whole.
Example 1 — Largest sector
Which drink did the most students choose?
Solution

The largest sector fills the most of the circle.

\(\dfrac{1}{2}>\dfrac{1}{3}>\dfrac{1}{6}\)Water
Example 2 — Count from a fraction
How many of the \(24\) students chose Water?
Solution

Multiply the fraction by the total.

\(\dfrac{1}{2}\times 24\)\(=\)\(12\)
Example 3 — Another sector
How many chose Juice, a third of the group?
Solution

Multiply the fraction by the total.

\(\dfrac{1}{3}\times 24\)\(=\)\(8\)
Example 4 — Sectors make a whole
Do the three fractions add to one whole?
Solution

Add over a common denominator of \(6\).

\(\dfrac{3}{6}+\dfrac{2}{6}+\dfrac{1}{6}\)\(=\)\(1\)

Common pitfalls

The whole circle is the total. Every sector is a part of the same whole group, so the fractions add to one.
Fraction, then multiply. A sector's count is its fraction of the total, not the number of sectors in the graph.
Bigger sector, bigger part. Compare how much of the circle each sector fills to see which is largest.

Frequently asked questions

What does the whole circle stand for?

The whole group. Every sector is a part of it, so all the sectors together make one whole.

How do I find how many a sector stands for?

Multiply the sector's fraction by the total. Water is a half of \(24\), so \(\dfrac{1}{2}\times 24 = 12\).

Which sector is the biggest category?

The one that fills the most of the circle. A bigger sector is a bigger fraction and a larger part of the group.

Do the fractions always add to one?

Yes. Because the sectors are the parts of one whole, their fractions add to one, and their counts add to the total.

Can a sector graph show percentages?

Yes. The same sectors can be read as fractions, as percentages that add to \(100\%\), or as numbers of people that add to the total.