What is pie chart angles that do not total 360^?

Always check that the sector angles add to 360^.

EnglandStatisticsSyllabus dot point

How do you organise raw data into clear tables and charts?

Frequency tables, grouped frequency tables, two-way tables, pictograms, bar charts and pie charts.

A focused answer to AQA GCSE Statistics on organising data, covering frequency and grouped frequency tables, two-way tables, pictograms, bar charts and pie charts, including how to calculate pie chart angles.

Generated by Claude Opus 4.89 min answerUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
Frequency and grouped frequency tables
Two-way tables
Pictograms and bar charts
Pie charts

What this dot point is asking

AQA wants you to organise raw data into frequency tables, grouped frequency tables and two-way tables, and to draw and read pictograms, bar charts and pie charts, including working out pie chart angles. These are the building blocks of the whole "processing and representing" module: a clean table is the first step before any average, diagram or comparison.

Frequency and grouped frequency tables

Grouping makes large or continuous data sets manageable and ready for a histogram, but it has a cost: once values are grouped you lose the exact figures, so the mean and median you calculate later are estimates rather than exact values. Class intervals must be written so that every value lands in exactly one class, which is why AQA uses the $0 \le t < 10$ , $10 \le t < 20$ style with strict inequalities at the top.

Two-way tables

A two-way table classifies data by two variables at once, for example gender against transport to school, with totals along each row and column. Reading and completing a two-way table is a frequent exam skill: a missing cell is found by using the fact that each row and column adds to its total, and the grand total ties everything together. Once complete, the table is a ready source of probabilities, as in the worked exam question above.

Pictograms and bar charts

The gaps on a bar chart matter: they signal that the categories are separate, which is correct for categorical or discrete data. Continuous data has no gaps because the classes run into one another, and that is drawn as a histogram instead. On a pictogram, the key lets you use part-symbols (half a symbol for half the key value), but without the key the diagram is meaningless.

Choosing between the diagrams is itself examined. A bar chart is best for comparing the frequencies of separate categories, a pie chart for showing each category's share of a whole, and a pictogram for an accessible, eye-catching display where exact precision is less important. Pie charts work well when there are only a few categories and you care about proportions, but they become hard to read with many thin sectors, where a bar chart is clearer. The frequency table sits behind all of them: a clean table is what you read the bar heights, pie angles and pictogram symbol counts from, so a careless table error feeds straight into every diagram you draw from it.

Pie charts

Calculating pie chart angles

In a survey of $40$ people, the travel choices were: cycling $10$ , bus $16$ , car $8$ , walk $6$ . We want to find the sector angle for each category so the pie chart can be drawn.

Step 1: Find the total frequency

Adding all four counts confirms the sample size and gives the denominator for every fraction:

10 + 16 + 8 + 6 = 40

Step 2: Find the angle each person represents

A full circle is $360^\circ$ , and there are $40$ people, so each person accounts for:

\frac{360^\circ}{40} = 9^\circ \text{ per person}

Step 3: Multiply each frequency by the angle per person

Scaling each frequency by $9^\circ$ converts it into a sector angle:

\text{cycling: } 10 \times 9 = 90^\circ, \quad \text{bus: } 16 \times 9 = 144^\circ

\text{car: } 8 \times 9 = 72^\circ, \quad \text{walk: } 6 \times 9 = 54^\circ

Step 4: Check the angles sum to 360 degrees

Always verify that all sectors account for the whole circle:

90 + 144 + 72 + 54 = 360^\circ \checkmark

Cycling takes a quarter of the pie because $\frac{10}{40} = \frac{1}{4}$ , which corresponds to $\frac{360^\circ}{4} = 90^\circ$ , a useful sense-check.

Final answer: the sector angles are cycling $90^\circ$ , bus $144^\circ$ , car $72^\circ$ , walk $54^\circ$ .

Exam-style practice questions

Practice questions written in the style of AQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

AQA 20193 marksIn a survey of

72

people about their favourite drink,

24

chose tea,

30

chose coffee and the rest chose juice. Calculate the angle each category would have in a pie chart.

Show worked answer →

Juice $= 72 - 24 - 30 = 18$ .

Each $1$ person is $\frac{360}{72} = 5^\circ$ .

Tea: $24 \times 5 = 120^\circ$ . Coffee: $30 \times 5 = 150^\circ$ . Juice: $18 \times 5 = 90^\circ$ .

Check: $120 + 150 + 90 = 360^\circ$ .

Markers reward finding the missing frequency, the angle per person (or $\frac{\text{frequency}}{72}\times 360$ ), and angles that total $360^\circ$ .

AQA 20214 marksA two-way table records gender against how pupils travel to school. Of

50

pupils,

28

are girls;

12

girls and

9

boys walk;

30

pupils in total walk. (a) Complete the table. (b) One pupil is chosen at random; find the probability the pupil is a boy who does not walk.

Show worked answer →

Boys $= 50 - 28 = 22$ . Pupils who do not walk $= 50 - 30 = 20$ . Boys who walk $= 9$ , so boys who do not walk $= 22 - 9 = 13$ .

(b) $P(\text{boy and does not walk}) = \frac{13}{50} = 0.26$ .

Markers reward using row and column totals to fill the missing cells (boys, non-walkers, boys not walking) and reading the required probability $\frac{13}{50}$ .

Related dot points

Sources & how we know this

AQA GCSE Statistics (8382) specification — AQA (2017)