Cumulative frequency: IGCSE Mathematics questions with answers
Free Cumulative frequency 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.
The lengths, L mm, of 80 leaves are summarised in the table.
Length (L mm)
0 < L ≤ 20
20 < L ≤ 40
40 < L ≤ 60
60 < L ≤ 80
80 < L ≤ 100
Frequency
8
p
q
r
12
Table 1.1
A cumulative frequency polygon is drawn: the cumulative frequencies are plotted at the upper class boundaries and the points are joined with straight lines. From the polygon, the median is 50 mm and the upper quartile is 72 mm. For n leaves, use the n2th value for the median, the n4th value for the lower quartile and the 3n4th value for the upper quartile.
(a)
Find the values of p, q and r.
[5]
(b)
Find the interquartile range.
[2]
(c)
More leaves are added to the original 80: m leaves with 0 < L ≤ 20 and k leaves with 80 < L ≤ 100. From the new polygon, the median is still 50 mm and the upper quartile is now 76 mm. Find m and k.
[5]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
p = 24, q = 16, r = 20
p + q + r = 60 B1 median in 40 < L ≤ 60: 8 + p + q2 = 40 M1 upper quartile in 60 < L ≤ 80: 60 + 20 × 60 − (8 + p + q)r = 72 M1 uses p + q = 60 − r to get r − 8r = 0.6, r = 20 A1 p = 24, q = 16 A1
5
(b)
42 mm (lower quartile 30 mm)
lower quartile: 20 + 20 × 1224 = 30 M1 42 A1
2
(c)
m = 8, k = 8
new cumulative frequencies 8 + m, 32 + m, 48 + m, 68 + m, 80 + m + k B1 median at 80 + m + k2 = 32 + m + 8 (halfway through the 40–60 class), giving k = m M1 upper quartile at 3(80 + 2m)4 = 60 + 1.5m, in the 60–80 class M1 60 + 20 × 60 + 1.5m − (48 + m)20 = 76, i.e. 72 + 0.5m = 76 M1 m = 8, k = 8 A1
5
Question 2Structured · 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
6
12
17
11
4
Table 2.1
(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)
6, 18, 35, 46, 50
at least 3 correct B1 6, 18, 35, 46, 50 B1
2
(b)
15
15 B1
1
(c)
48
midpoints 10, 30, 50, 70, 90 M1 Σfx ÷ Σf M1 48 A1
3
Question 3Structured · 5 marks
The cumulative frequency diagram shows information about the times, t minutes, that 77 students took to travel to school.
Fig. 3.1
(a)
Find the median.
[1]
(b)
Find the interquartile range.
[2]
(c)
Find the number of students who took more than 45 minutes.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
28 (accept 26 to 30)
28 (accept 26 to 30) B1
1
(b)
18 (accept 16 to 20)
UQ ≈ 38 and LQ ≈ 20 seen M1 18 (accept 16 to 20) A1
2
(c)
11 (accept 9 to 13)
77 − their reading at t = 45 M1 11 A1
2
Question 4Structured · 5 marks
The cumulative frequency diagram shows information about the times, t minutes, that 86 students took to travel to school.
Fig. 4.1
(a)
Find the median.
[1]
(b)
Find the interquartile range.
[2]
(c)
Find the number of students who took more than 45 minutes.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
29 (accept 27 to 31)
29 (accept 27 to 31) B1
1
(b)
17 (accept 15 to 19)
UQ ≈ 38 and LQ ≈ 21 seen M1 17 (accept 15 to 19) A1
2
(c)
11 (accept 9 to 13)
86 − their reading at t = 45 M1 11 A1
2
Question 5Structured · 5 marks
The cumulative frequency diagram shows information about the times, t minutes, that 94 students took to travel to school.
Fig. 5.1
(a)
Find the median.
[1]
(b)
Find the interquartile range.
[2]
(c)
Find the number of students who took more than 45 minutes.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
28 (accept 26 to 30)
28 (accept 26 to 30) B1
1
(b)
17 (accept 15 to 19)
UQ ≈ 37 and LQ ≈ 21 seen M1 17 (accept 15 to 19) A1
2
(c)
11 (accept 9 to 13)
94 − their reading at t = 45 M1 11 A1
2
Question 6Structured · 5 marks
The cumulative frequency diagram shows information about the times, t minutes, that 65 students took to travel to school.
Fig. 6.1
(a)
Find the median.
[1]
(b)
Find the interquartile range.
[2]
(c)
Find the number of students who took more than 45 minutes.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
28 (accept 26 to 30)
28 (accept 26 to 30) B1
1
(b)
16 (accept 14 to 18)
UQ ≈ 38 and LQ ≈ 21 seen M1 16 (accept 14 to 18) 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