IGCSE · Mathematics 0580 · Topic

Statistics: IGCSE Mathematics questions and answers

Q: What is in IGCSE Mathematics Statistics?

In the 0580 syllabus, Statistics covers Averages & measures of spread, Scatter diagrams, Cumulative frequency, Histograms.

Q: Where can I get Statistics questions with mark schemes?

This page has 10 Statistics questions with answers. For more, the free generator on mentorriyaz.in builds a new Statistics paper with a full mark scheme each time you click.

10 free IGCSE Mathematics Statistics questions written in the style of Cambridge Mathematics papers, each with its answer and mark scheme. 4 of them are A* challenge questions, built to catch the mistakes strong students still make.

This topic covers Averages & measures of spread, Scatter diagrams, Cumulative frequency, Histograms. Work through the questions below, then generate a full Statistics paper with a fresh set every time.

Generate a full Statistics paper →

Statistics sub-topics

Averages & measures of spread Scatter diagrams Cumulative frequency Histograms

Statistics practice questions

Question 1Structured · 8 marksA* challenge

The table shows information about the times, t minutes, that some customers spent in a shop.

Time (t minutes)	0 < t ≤ 10	10 < t ≤ 20	20 < t ≤ 40	40 < t ≤ 60	60 < t ≤ 100
Frequency		10	20	60	120
Frequency density	2.5

Table 1.1

(a)

Complete the table.

[3]

(b)

Calculate an estimate of the number of customers who spent more than 50 minutes in the shop.

[2]

(c)

Calculate an estimate of the mean time.

[3]

Show answers and mark scheme

Part	Answer and marking points	Marks
(a)	frequency 25; densities 1, 1, 3, 3 25 B1 all frequency densities correct B2 B1 for at least two correct	3
(b)	150 ½ × 60 + later frequencies M1 150 A1	2
(c)	57.3 min midpoints used M1 Σfx ÷ Σf M1 57.3 A1	3

Question 2Structured · 3 marksA* challenge

In a histogram, the bar for the class 40 < x ≤ 60 has height 1.5 (frequency density). The bar for 30 < x ≤ 40 represents 18 people. Find the number of people in the class 40 < x ≤ 60, and the height of the bar for 30 < x ≤ 40.

[3]

Show answers and mark scheme

Part	Answer and marking points	Marks
	30; 1.8 1.5 × 20 M1 30 A1 18 ÷ 10 = 1.8 B1	3

Question 3Structured · 7 marksA* challenge

The histogram for the times, t minutes, that 112 people waited at a clinic has these frequency densities:

time (t minutes)	0 < t ≤ 10	10 < t ≤ 15	15 < t ≤ 20	20 < t ≤ 30	30 < t ≤ 50
frequency density	1.6	4	7.2	2.4	0.8

Table 3.1

(a)

Find the number of people in each class.

[2]

(b)

Estimate the number of people who waited more than 25 minutes.

[2]

(c)

Calculate an estimate of the mean waiting time.

[3]

Show answers and mark scheme

Part	Answer and marking points	Marks
(a)	16, 20, 36, 24, 16 frequency = frequency density × class width M1 16, 20, 36, 24, 16 A1	2
(b)	28 uses a fraction of the class containing 25 M1 28 A1	2
(c)	19.6 min midpoints 5, 12.5, 17.5, 25, 40 M1 Σfx ÷ 112 M1 19.6 A1	3

Question 4Structured · 3 marksA* challenge

The mean mass of 15 boys is 43 kg.
The mean mass of 9 girls is 47 kg.
One more student joins the group. The mean mass of all 25 students is now 44.6 kg.
Find the mass of the student who joined.

[3]

Show answers and mark scheme

Part	Answer and marking points	Marks
	47 kg 15 × 43 + 9 × 47 = 1068 M1 25 × 44.6 = 1115 M1 47 A1	3

Question 5Structured · 5 marks

Here are the marks, out of 20, of 7 students in a quiz.
20, 19, 13, 20, 20, 3, 13

(a)

Write down the mode.

[1]

(b)

Find the median.

[1]

(c)

Calculate the mean.

[2]

(d)

Find the range.

[1]

Show answers and mark scheme

Part	Answer and marking points	Marks
(a)	20 20 B1	1
(b)	19 19 B1	1
(c)	15.4 108 ÷ 7 M1 15.4 A1	2
(d)	17 17 B1	1

Question 6Structured · 4 marks

The scatter diagram shows test mark against hours of revision for 10 cases.

Fig. 6.1

(a)

What type of correlation is shown?

[1]

(b)

Draw a line of best fit on the diagram.

[1]

(c)

Use your line of best fit to estimate the test mark when hours of revision is 4.

[1]

(d)

Explain why it may not be reliable to use your line to estimate the value when x = 20.

[1]

Show answers and mark scheme

Part	Answer and marking points	Marks
(a)	Positive Positive B1	1
(b)	Ruled line through the trend of the points Ruled line of best fit within the shaded tolerance B1	1
(c)	49.2 (accept 44.2 to 54.2) Value from their line, in range B1	1
(d)	It is outside the range of the data (extrapolation) Outside the range of the data B1	1

Question 7Structured · 3 marks

The table shows the times (t minutes) taken by some students to complete a puzzle.

Time (t min)	0 < t ≤ 10	10 < t ≤ 20	20 < t ≤ 40	40 < t ≤ 70
Frequency	9	12	20	14

Table 7.1

(a)

Calculate the frequency density for each class.

[2]

(b)

Explain why a histogram is used rather than a bar chart.

[1]

Show answers and mark scheme

Part	Answer and marking points	Marks
(a)	0.9, 1.2, 1, 0.467 frequency ÷ class width M1 0.9, 1.2, 1, 0.467 A1	2
(b)	unequal class widths classes have unequal widths B1	1

Question 8Structured · 5 marks

The cumulative frequency diagram shows information about the times, t minutes, that 89 students took to travel to school.

Fig. 8.1

(a)

Find the median.

[1]

(b)

Find the interquartile range.

[2]

(c)

Find the number of students who took more than 35 minutes.

[2]

Show answers and mark scheme

Part	Answer and marking points	Marks
(a)	27 (accept 25 to 29) 27 (accept 25 to 29) B1	1
(b)	18 (accept 16 to 20) UQ ≈ 38 and LQ ≈ 19 seen M1 18 (accept 16 to 20) A1	2
(c)	27 (accept 25 to 29) 89 − their reading at t = 35 M1 27 A1	2

Question 9Structured · 5 marks

The table shows the times, t minutes, that some patients waited at a clinic.

Time (t minutes)	Frequency	Frequency density
0 < t ≤ 10	9
10 < t ≤ 15	20
15 < t ≤ 20	24
20 < t ≤ 30	22
30 < t ≤ 50	6

Table 9.1

(a)

Complete the frequency density column.

[2]

(b)

On the grid, draw a histogram to show this information.

Fig. 9.1

[3]

Show answers and mark scheme

Part	Answer and marking points	Marks
(a)	0.9, 4, 4.8, 2.2, 0.3 All correct B2 B1 for three correct	2
(b)	See histogram Correct class widths B1 Correct heights (B1 for three correct) B2	3

Question 10Structured · 6 marks

The table shows the masses (m grams) of some apples.

Mass (m g)	0 < m ≤ 20	20 < m ≤ 40	40 < m ≤ 60	60 < m ≤ 80	80 < m ≤ 100
Frequency	5	10	18	12	6

Table 10.1

(a)

Complete the cumulative frequency table.

[2]

(b)

Write down the number of apples with mass more than 60 g.

[1]

(c)

Calculate an estimate of the mean mass.

[3]

Show answers and mark scheme

Part	Answer and marking points	Marks
(a)	5, 15, 33, 45, 51 at least 3 correct B1 5, 15, 33, 45, 51 B1	2
(b)	18 18 B1	1
(c)	51.57 midpoints 10, 30, 50, 70, 90 M1 Σfx ÷ Σf M1 51.57 A1	3

Frequently asked questions

What is in IGCSE Mathematics Statistics?

In the 0580 syllabus, Statistics covers Averages & measures of spread, Scatter diagrams, Cumulative frequency, Histograms.

Where can I get Statistics questions with mark schemes?

This page has 10 Statistics questions with answers. For more, the free generator on mentorriyaz.in builds a new Statistics paper with a full mark scheme each time you click.

Want a mentor, not just a paper?

Riyaz Shaikh has mentored IGCSE, IB and A Level students for 15+ years, one-on-one, online and in Mumbai. The hardest questions on this site are the ones he uses to find a student's weak points.

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Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in

Statistics: IGCSE Mathematics questions and answers

Statistics sub-topics

Statistics practice questions

Other IGCSE Mathematics topics

Frequently asked questions

What is in IGCSE Mathematics Statistics?

Where can I get Statistics questions with mark schemes?

Want a mentor, not just a paper?