Why is the tea sector 90° and not 15° when 15 of 60 people chose tea?

Because a pie chart is a full circle of 360°, and the angle is measured out of 360 — not out of the number of people. The 60 people fill the whole 360° circle. The 15 who chose tea are a quarter of the people, so the tea sector is a quarter of the circle: (15 ÷ 60) × 360 = 90°. Writing 15° copies the frequency straight onto the chart, but 15 is a count of people, not a slice of 360°.

How do you find how many people a pie-chart sector represents from its angle?

Use freq = (angle ÷ 360) × total. The angle as a fraction of 360° is the same fraction of the people. For example, an 80° sector on a chart of 90 people is (80 ÷ 360) × 90 = 20 people. Reading 80 straight off the angle is wrong — the angle is out of 360, never the count.

How do you turn a pie-chart angle into a percentage?

Use pct = (angle ÷ 360) × 100. The angle as a fraction of 360° scales onto 100 for a percentage. A 90° sector is (90 ÷ 360) × 100 = 25%. A single sector can never be more than 100%, so an answer like 162% from a 162° angle is a flag that the angle was read off directly instead of converted — the correct value is (162 ÷ 360) × 100 = 45%.

GCSE Maths Foundation · AQA · Statistical diagrams

Pie chart angles and frequency: why the angle is out of 360, not the number of people

Pie-chart questions trip students who treat the angle, the frequency and the percentage as one interchangeable number. Asked for the angle of the sector for 15 of 60 people, they write 15° — copying the frequency onto the chart. Asked how many people an 80° sector represents, they answer 80. Asked for the percentage of a 162° sector, they answer 162% — a value that is impossible for a single sector.

The thirty-second fix: the angle is always out of 360°. To build a sector, angle = (freq ÷ total) × 360. To read a frequency, freq = (angle ÷ 360) × total. For a percentage, pct = (angle ÷ 360) × 100.

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How to spot it in your own work

You gave $15^\circ$ as the tea sector for 15 of 60 people — copying the frequency straight onto the chart instead of converting.
You read an angle straight off as the number of people — answering $80$ for an $80^\circ$ sector rather than $(80 \div 360) \times \text{total}$ .
You gave a percentage above 100 (such as $162\%$ for a $162^\circ$ sector) — a sign the angle was read off rather than scaled onto 100.
You treated a frequency of 132 people as an angle of $132^\circ$ on any chart, ignoring the total.

An exam question that triggers it

Here is the canonical AQA Foundation trigger (Jun22 P2 Q16 shape — construct a pie chart):

In a survey of 60 people, 15 chose tea. What is the angle of the tea sector on a pie chart?

The misconception answer is $15^\circ$ — the frequency copied straight onto the chart. But the angle is measured out of the whole $360^\circ$ circle.

The 15 who chose tea are a quarter of the 60 people, so the sector is a quarter of the circle: $(15 \div 60) \times 360 = 90^\circ$ .

Why students fall for this

A pie chart hides its scale. The numbers in the question count people; the numbers on the chart measure degrees out of 360. Because both are “just numbers,” the student collapses them into one, and the conversion step — multiplying or dividing by 360 — never happens.

The reverse error has the same root. Given a sector angle, the student reads it straight off as a count or a percentage, because the angle “looks like the answer.” The hidden step “the angle is a fraction of 360°, so scale it by the total (for people) or by 100 (for a percentage)” is invisible — nothing on the chart announces it.

AQA Foundation papers exploit both directions: constructing sectors from frequencies (Jun22 P2 Q16), reading frequencies and percentages back off a chart (Nov24 P2 Q14), wording a difference between two sectors (Jun23 P3 Q22), and converting an angle to a percentage (Jun24 P3 Q25).

The fix: The angle is out of 360: scale by the total or by 100

Frequency → angle: angle = (freq ÷ total) × 360. For 15 of 60 people: $(15 \div 60) \times 360 = 90^\circ$ . A quarter of the people is a quarter of the circle.

Angle → frequency: freq = (angle ÷ 360) × total. An $80^\circ$ sector on a chart of 90 people is $(80 \div 360) \times 90 = 20$ people. Never read the angle off as the count.

Angle → percentage: pct = (angle ÷ 360) × 100. A $90^\circ$ sector is $(90 \div 360) \times 100 = 25\%$ . A single sector can never exceed 100%.

Worked example

Find the angle of the tea sector when 15 of 60 people chose tea.

Write the fraction of people.
$\frac{15}{60} = \frac{1}{4}$
Scale that fraction onto the 360° circle.
$\frac{15}{60} \times 360$
Calculate the angle.
$\text{Angle} = 90^\circ$

The trap answer $15^\circ$ copies the frequency onto the chart. The frequency counts people; the angle measures a slice of 360°. They are different units, so you always convert.

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Common questions

How do I turn a frequency into a pie-chart angle?: Divide the frequency by the total to get the fraction of people, then multiply by 360: $\text{angle} = (\text{freq} \div \text{total}) \times 360$ . For 9 of 60 people: $(9 \div 60) \times 360 = 54^\circ$ .
A sector is 120° on a pie chart of 72 people. How many people does it represent?: Use $\text{freq} = (\text{angle} \div 360) \times \text{total}$ . Here $(120 \div 360) \times 72 = 24$ people. The angle $120$ is not the count — it is a third of the circle, so it is a third of the 72 people.
Can a single sector ever be more than 100% or more than 360°?: No. The sectors of one pie chart always add to $360^\circ$ and to 100%. An answer like $162\%$ for a $162^\circ$ sector means the angle was read off directly; the correct value is $(162 \div 360) \times 100 = 45\%$ .
Is a frequency of 132 the same as an angle of 132°?: Only by coincidence at one particular total. On a chart of 720 people, $360 \div 720 = 0.5^\circ$ represents one person, so 132 people is $132 \times 0.5 = 66^\circ$ — not 132°. The angle always depends on the total.

Related misconceptions

Computing mean and median: why you must sort before finding the middleAnother statistics recipe with a hidden structural step — the same 'apply the method, do not copy the visible number' habit that pie-chart conversions demand.
Interpreting range and spread: why the range is a single number, not an intervalA neighbouring statistics misconception where students read a value off the surface instead of computing the quantity the question asks for.
Confusing statistical measures: why the mean, median, mode and range are not interchangeableThe same conflation reflex — treating distinct statistical quantities as one — that makes students swap a pie-chart angle for a frequency or a percentage.

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