Cumulative frequency Quiz (Grade 6)

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Cumulative frequency — Notes & Worked Examples Show / Hide

Explanation:

Cumulative frequency is a running total of the frequencies. Always plot cumulative frequency points at the upper bound (end value) of each class interval—never the midpoint—and join them with a smooth S-shaped curve.

For a total of N items, read across from N2 (50%) for the Median, from N4 (25%) for the Lower Quartile (LQ), and from 3N4 (75%) for the Upper Quartile (UQ). Then IQR = UQ − LQ.

Example 1: Complete the cumulative frequency table for the times (t mins) of 80 runners.

Solution:

Time (t)	0<t≤20	20<t≤30	30<t≤40	40<t≤60
Freq.	12	28	26	14
Cum. Freq.	12	40	66	80

Plot at upper bounds: (20, 12), (30, 40), (40, 66), (60, 80).

Example 2: From the curve for N = 80, CF = 20 gives 24 mins and CF = 60 gives 37 mins. Find the median and IQR.

Solution:

Median (CF = 40) = 30 mins; LQ = 24, UQ = 37

IQR = 37 − 24 = 13 mins → Answer: Median 30, IQR 13 mins

One Page Guide (PDF) Cumulative frequency Worksheets

Question 1

[1 mark]

From a cumulative frequency graph of 80 test scores, the lower quartile (at cumulative frequency 20) is 21 and the upper quartile (at cumulative frequency 60) is 48.
Work out the interquartile range (IQR).

Worked Solution & Answer

IQR = UQ - LQ = 48 - 21 = 27 B1

Answer: 27

Question 2

[1 mark]

From a cumulative frequency graph of 80 test scores, the lower quartile (at cumulative frequency 20) is 25 and the upper quartile (at cumulative frequency 60) is 52.
Work out the interquartile range (IQR).

Worked Solution & Answer

IQR = UQ - LQ = 52 - 25 = 27 B1

Answer: 27

Question 3

[2 marks]

The cumulative frequency graph shows information about the weights of 60 potatoes.

(a) Use the graph to find an estimate for the median weight. [1 mark]

(b) Is Jamil correct?
You must give a reason for your answer. [1 mark]

Worked Solution & Answer

(a)

Read at CF = 30 → 57 g B1

Answer (a): 57 g

(b)

Grouped data: actual min and max are unknown C1

Answer (b): No (he might not be correct), because the lightest potato could weigh less than 40 g and the heaviest could weigh less than 80 g

Question Paper (PDF) • Mark Scheme (PDF)

Question 4

[3 marks]

The cumulative frequency table gives information about the ages of 80 people working for a company.

(a) On the grid below, draw a cumulative frequency graph for this information. [2 marks]

(b) Use your graph to find an estimate for the median age. [1 mark]

years

Worked Solution & Answer

(a)

Plot points (30, 20), (40, 48), (50, 64), (60, 75), (70, 80) at upper bounds M1 A1

Answer (a): Points (30, 20), (40, 48), (50, 64), (60, 75), (70, 80) plotted and joined with a smooth curve or line segments

(b)

reading across from cumulative frequency = 40 gives ~37 years B1

Answer (b): 37 (accept 36 to 38) years

Question Paper (PDF) • Mark Scheme (PDF)

Question 5

[3 marks]

The cumulative frequency table gives information about the heights, in cm, of 40 plants.

(a) On the grid, draw a cumulative frequency graph for this information. [2 marks]

(b) Use the graph to find an estimate for the median height of the plants. [1 mark]

Worked Solution & Answer

(a)

Plot upper bounds (5,4), (10,11), (15,24), (20,34), (25,38), (30,40) M1 A1

Answer (a): Points (5, 4), (10, 11), (15, 24), (20, 34), (25, 38), (30, 40) plotted and joined

(b)

Read off at CF = 20 ⇒ 13.5 cm B1

Answer (b): 13.5 cm

Question Paper (PDF) • Mark Scheme (PDF)

Question 6 IGCSE Nov 2023 1H Q13

[4 marks]

The cumulative frequency graph gives information about the times, in seconds, that 80 adults took to log in to an online bank.

(a) Find an estimate for the median time. [1 mark]

seconds

(b) Work out the percentage of these adults that took longer than 50 seconds to log in.
Show your working clearly. [3 marks]

Worked Solution & Answer

(a)

At CF = 40, time = 25 seconds B1

Answer (a): 25 seconds

(b)

At time = 50 s, CF = 75 M2
Number taking longer than 50 s = 80 − 75 = 5. Percentage = (5 ÷ 80) × 100 = 6.25% A1

Answer (b): 6.25 %

Question Paper (PDF) • Mark Scheme (PDF)

Question 7 AQA Nov 2023 2H Q17

[4 marks]

190 people were asked how much they spent on takeaways one month.
The table shows information about the results.
@@TABULAR₀@@

(a) How many people spent **more** than £20 ? [2 marks]

Answer

(b) Farah draws this cumulative frequency curve to represent the results. [2 marks]

Give **two** criticisms of her graph.

Worked Solution & Answer

(a)

190 – 64 = 126 M1 A1

Answer (a): Answer 126

(b)

Criticism 1: Vertical axis is labelled "Frequency" instead of "Cumulative frequency" M1
Criticism 2: At x = 50, the curve is plotted at 200 instead of 190 A1

Answer (b): Criticism 1: The vertical axis is labelled Frequency instead of Cumulative frequency
Criticism 2: The final point is plotted at (50, 200) instead of (50, 190)

Question Paper (PDF) • Mark Scheme (PDF)

Question 8 AQA Nov 2020 2H Q17

[4 marks]

The cumulative frequency graph shows information about the masses of 200 apples.

(a) Estimate the median mass. [1 mark]

Answer grams

(b) Apples with mass 90 grams or less cost 32p each.
Apples with mass more than 90 grams cost 39p each.
Estimate the total cost of the 200 apples. [3 marks]

Answer £

Worked Solution & Answer

(a)

Half of 200 is 100
Reading across from cumulative frequency 100 to the curve gives approximately 83.5 grams (allow 83 to 84 g). B1

Answer (a): Answer 83.5 grams

(b)

At mass 90 grams, cumulative frequency = 154 M1
Number of apples ≤ 90 g = 154 M1
Number of apples > 90 g = 200 - 154 = 46
Cost = 154 × £0.32 + 46 × £0.39 = £49.28 + £17.94 = £67.22 (or ~£67 to £68). A1

Answer (b): Answer £ 67.36

Question Paper (PDF) • Mark Scheme (PDF)

Question 9 IGCSE Jun 2023 1H Q12

[4 marks]

The cumulative frequency graph shows information about the heights, in centimetres, of 50 plants in a flowerbed.

(a) Use the graph to find an estimate for the median height of these plants. [1 mark]

centimetres

(b) Use the graph to find the frequency for the class interval 30 < Height ≤ 40 [1 mark]

Worked Solution & Answer

(a)

At CF = 25, height = 28 cm B1

Answer (a): 28 centimetres

(b)

CF(40) – CF(30) = 44 – 30 = 14 B1

Answer (b): 14

(c)

50 – CF(35) = 50 – 38 = 12 M1 A1

Answer (c): 12

Question Paper (PDF) • Mark Scheme (PDF)

Question 10 AQA Jun 2025 3H Q13

[5 marks]

The table shows information about the salary of 90 employees.
@@TABULAR₀@@

(a) Complete the cumulative frequency table.
@@TABULAR₀@@ [1 mark]

(b) Draw a cumulative frequency diagram to represent the data. [2 marks]

Answer

Worked Solution & Answer

(a)

Cumulative frequencies: 66 + 14 = 80, 80 + 5 = 85, 85 + 2 = 87, 87 + 3 = 90 B1

Answer (a): 80, 85, 87, 90

(b)

Plot (20k, 44), (40k, 66), (60k, 80), (80k, 85), (100k, 87), (120k, 90) M1 A1

Answer (b): Points plotted at upper bounds and joined with a smooth curve or straight line segments.

(c)

Reading at s = 32 000 gives approximately 58 employees M1 A1

Answer (c): Answer 58 (accept [55, 60])

Question Paper (PDF) • Mark Scheme (PDF)

Score: 0 / 10 (0 / 31 marks)

Cumulative frequency Worksheets Next: Box plots →

Grade 6 Quizzes

14 Topics

6A - Recurring decimals	6B - Harder indices
6C - The product rule	6D - Repeated change
6E - Triple brackets	6F - Parallel and perpendicular
6G - Inequalities on graphs	6H - Similar shapes (area and vol)
6J - Negative scale factors	6K - Circle theorems
6L - Cumulative frequency	6M - Box plots
6N - Combined transformations	6P - Capture recapture