Charts, tables and diagrams

Visual model

Choose the chart that matches the data

bar chartcomparepie chart

Gold-standard guide

20 mins

What you will learn

Read and create clear statistical displays.

Use a clear step-by-step method for charts, tables and diagrams.

Check your answer and avoid the most common exam mistake.

Useful before you start

Core number skillsEarlier statistics skillsShowing clear working

Core knowledge

Know the rule, then use it

These are the short notes. Read each one, then check you can use it in the worked example below.

Method

$Pie$ chart: angle for a category = (frequency/total) × 360°

Step 1

Use the pie chart formula in reverse

Frequency = (angle/360) × total = ( $7\frac{5}{3}60$ ) × 120 = 25 students

Step 2

Check the method

$7\frac{5}{3}60$ = $\frac{5}{2}4$ of the students

Watch out

Students divide 120 by 75 directly, giving 1.6

Pie

chart angle

$sector angle = frequenc\frac{y}{total} \times 360.$

Bar chart

Use equal-width bars for categories.

Worked example

A $pie$ chart represents 120 students. The sector for 'reading' has an angle of 75°. Find the number of students who chose reading.

Use the $pie$ chart formula in reverse: Frequency = (angle/360) × total = ( $7\frac{5}{3}60$ ) × 120 = 25 students.

Check the method: $7\frac{5}{3}60$ = $\frac{5}{2}4$ of the students. $\frac{5}{2}4$ × 120 = 25. ✓

Final answer

25 students

Question ladder

Build up to the hardest questions

Do them in order. If you miss a step, read the solution, then redo the question without looking.

Workedreasoning

A $pie$ chart represents 120 students. The sector for 'reading' has an angle of 75°. Find the number of students who chose reading.

3 marks4 minscharts-tables-and-diagrams-worked

Show solution

Worked solution

1.Use the $pie$ chart formula in reverse: Frequency = (angle/360) × total = ( $7\frac{5}{3}60$ ) × 120 = 25 students.
2.Check the method: $7\frac{5}{3}60$ = $\frac{5}{2}4$ of the students. $\frac{5}{2}4$ × 120 = 25. ✓

Final answer

25 students

Mark points

M1: use the $pie$ chart formula in reverse
M1: check the method
A1: 25 students

Watch out

6. Always set up the fraction (angle/360) first, then multiply by the total.The angle is a fraction of 360°, not a fraction of the total directly.

Diagnosticrecall

Total 80 students; sport angle = 108°. How many chose sport?

1 mark2 minscharts-tables-and-diagrams-q1

Show solution

Worked solution

1.Spot the skill: $Pie$ chart: angle for a category = (frequency/total) × 360°.
2.Use the use the $pie$ chart formula in reverse stage first, then check the method.
3.Keep the final answer visible: 24.

Final answer

Mark points

M1: use the correct $pie$ chart: angle for a category = (frequency/total) × 360°.bar chart: frequency is the height of each bar. stem-and-leaf: each leaf is a digit, enabling quick median and range.two-way table: rows and columns give joint and marginal frequencies.
A1: 24

Watch out

6. Always set up the fraction (angle/360) first, then multiply by the total.The angle is a fraction of 360°, not a fraction of the total directly.

Easyprocedure

24 out of 60 students chose maths. Find the $pie$ chart angle for maths.

2 marks3 minscharts-tables-and-diagrams-q2

Show solution

Worked solution

1.Spot the skill: $Pie$ chart: angle for a category = (frequency/total) × 360°.
2.Use the check the method stage first, then use the $pie$ chart formula in reverse.
3.Keep the final answer visible: 144°.

Final answer

144°

Mark points

M1: use the correct $pie$ chart: angle for a category = (frequency/total) × 360°.bar chart: frequency is the height of each bar. stem-and-leaf: each leaf is a digit, enabling quick median and range.two-way table: rows and columns give joint and marginal frequencies.
A1: 144°

Watch out

6. Always set up the fraction (angle/360) first, then multiply by the total.The angle is a fraction of 360°, not a fraction of the total directly.

Mediumreasoning

A stem-and-leaf: 3|4 5 7, 4|1 2 8, 5|0 6. Find the median and range.

3 marks4 minscharts-tables-and-diagrams-q3

Show solution

Worked solution

1.Spot the skill: $Pie$ chart: angle for a category = (frequency/total) × 360°.
2.Use the use the $pie$ chart formula in reverse stage first, then check the method.
3.Keep the final answer visible: Median = 42; Range = 56 − 34 = 22.

Final answer

Median = 42; Range = 56 − 34 = 22

Mark points

M1: use the correct $pie$ chart: angle for a category = (frequency/total) × 360°.bar chart: frequency is the height of each bar. stem-and-leaf: each leaf is a digit, enabling quick median and range.two-way table: rows and columns give joint and marginal frequencies.
A1: Median = 42; Range = 56 − 34 = 22

Watch out

6. Always set up the fraction (angle/360) first, then multiply by the total.The angle is a fraction of 360°, not a fraction of the total directly.

Hardproblem solving

A back-to-back stem-and-leaf shows boys' scores and girls' scores. How do you compare distributions?

3 marks5 minscharts-tables-and-diagrams-q4

Show solution

Worked solution

1.Spot the skill: $Pie$ chart: angle for a category = (frequency/total) × 360°.
2.Use the check the method stage first, then use the $pie$ chart formula in reverse.
3.Keep the final answer visible: Compare medians and ranges for each group.

Final answer

Compare medians and ranges for each group

Mark points

M1: use the correct $pie$ chart: angle for a category = (frequency/total) × 360°.bar chart: frequency is the height of each bar. stem-and-leaf: each leaf is a digit, enabling quick median and range.two-way table: rows and columns give joint and marginal frequencies.
A1: Compare medians and ranges for each group

Watch out

6. Always set up the fraction (angle/360) first, then multiply by the total.The angle is a fraction of 360°, not a fraction of the total directly.

Exam-stylemulti-step

A two-way table shows 45 males, 55 females, 30 prefer tea, 70 prefer coffee. If 20 males prefer tea, find P(female and coffee).

4 marks6 minscharts-tables-and-diagrams-q5

Show solution

Worked solution

1.Spot the skill: $Pie$ chart: angle for a category = (frequency/total) × 360°.
2.Use the use the $pie$ chart formula in reverse stage first, then check the method.
3.Keep the final answer visible: $3\frac{5}{1}00$ = $\frac{7}{2}0$ .

Final answer

$3\frac{5}{1}00$ = $\frac{7}{2}0$

Mark points

M1: use the correct $pie$ chart: angle for a category = (frequency/total) × 360°.bar chart: frequency is the height of each bar. stem-and-leaf: each leaf is a digit, enabling quick median and range.two-way table: rows and columns give joint and marginal frequencies.
A1: $3\frac{5}{1}00$ = $\frac{7}{2}0$

Watch out

6. Always set up the fraction (angle/360) first, then multiply by the total.The angle is a fraction of 360°, not a fraction of the total directly.

Grade 9 stretchproblem solving

A $pie$ -chart sector has angle 54 degrees and represents 36 people. Find the total number of people.

4 marks7 minschart-g9

Show solution

Worked solution

1.Find how many times the sector fits into 360 degrees.
2.Scale the frequency by the same amount.

Final answer

240

Mark points

M1: use $36\frac{0}{5}4$
M1: scale 36
A1: 240

Watch out

Do not rush straight into arithmetic. Select the relevant method and show a complete chain of working.

Timed checkpoint

12 mins - 9 marks

Switch between skills

Set a timer and attempt all four questions before opening any answers. This is closer to the way skills appear in a real paper.

1Charts, tables and diagrams - 2 marksTotal 80 students; sport angle = 108°. How many chose sport?Mark answer

Answer

2Collecting and sampling data - 2 marksWhy might a questionnaire question be biased?Mark answer

Answer

Leading wording, only offering responses that agree, or not including a 'no' option

3Averages and range - 2 marksThe mean of 5 numbers is 12. Four of them are 8, 14, 10, 15. Find the fifth.Mark answer

Answer

4Grouped data and estimated mean - 3 marksA survey records [10,20): 5 responses and [20,30): 15. Estimate total mean across both groups.Mark answer

Answer

Use midpoints 15 and 25: (5×15 + 15×25)/20 = $45\frac{0}{2}0$ = 22.5

Mastery check

I can explain the method for charts, tables and diagrams.
I can show clear working without skipping key steps.
6. Always set up the fraction (angle/360) first, then multiply by the total.The angle is a fraction of 360°, not a fraction of the total directly.

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Choose the chart that matches the data

What you will learn

Know the rule, then use it

Method

Use the pie chart formula in reverse

Check the method

Watch out

A piepiepie chart represents 120 students. The sector for 'reading' has an angle of 75°. Find the number of students who chose reading.

Build up to the hardest questions

Switch between skills

Get help with anything that still feels tricky.

A $pie$ chart represents 120 students. The sector for 'reading' has an angle of 75°. Find the number of students who chose reading.