Histograms: IGCSE Mathematics questions with answers
Free Histograms questions for IGCSE Mathematics (0580), Extended tier (Supplement content), part of Statistics. Each question has the answer and the marking points an examiner would look for.
In a histogram, the bar for the class 40 < x ≤ 60 has height 2.4 (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
48; 1.8
2.4 × 20 M1 48 A1 18 ÷ 10 = 1.8 B1
3
Question 3Structured · 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
17
10 < t ≤ 15
17
15 < t ≤ 20
19
20 < t ≤ 30
14
30 < t ≤ 50
13
Table 3.1
(a)
Complete the frequency density column.
[2]
(b)
On the grid, draw a histogram to show this information.
Fig. 3.1
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
1.7, 3.4, 3.8, 1.4, 0.65
All correct B2 B1 for three correct
2
(b)
See histogram
Correct class widths B1 Correct heights (B1 for three correct) B2
3
Question 4Structured · 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
8
11
24
9
Table 4.1
(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)
0.8, 1.1, 1.2, 0.3
frequency ÷ class width M1 0.8, 1.1, 1.2, 0.3 A1
2
(b)
unequal class widths
classes have unequal widths B1
1
Question 5Structured · 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
15
40
50
120
Frequency density
1.5
Table 5.1
(a)
Complete the table.
[3]
(b)
Calculate an estimate of the number of customers who spent more than 15 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 15; densities 1.5, 2, 2.5, 3
15 B1 all frequency densities correct B2 B1 for at least two correct
3
(b)
218
½ × 15 + later frequencies M1 218 A1
2
(c)
56.7 min
midpoints used M1 Σfx ÷ Σf M1 56.7 A1
3
Question 6Structured · 7 marksA* challenge
The histogram for the times, t minutes, that 118 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
5.6
6
3.6
0.4
Table 6.1
(a)
Find the number of people in each class.
[2]
(b)
Estimate the number of people who waited more than 12 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, 28, 30, 36, 8
frequency = frequency density × class width M1 16, 28, 30, 36, 8 A1
2
(b)
90.8 (accept 91)
uses a fraction of the class containing 12 M1 90.8 or 91 A1
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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