IB · Mathematics: Applications & Interpretation SL & HL · Statistics & probability

Descriptive statistics: IB Mathematics: Applications & Interpretation questions with answers

Free Descriptive statistics questions for IB Mathematics: Applications & Interpretation (SL & HL), part of Statistics & probability. Each question has the answer and the marking points an examiner would look for.

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Descriptive statistics practice questions

Question 1Structured · 5 marksA* challenge

A set of 17 marks has mean 53 and standard deviation 7.

(a)

Each mark is multiplied by 3 and then 5 is subtracted. Find the new mean and standard deviation.

[3]
(b)

A second group of 25 students has a mean mark of 49 on the original test. Find the mean mark of all 42 students.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)mean 154, sd 21
mean = 3 × 53 − 5 = 154 A1
adding does not change the sd (M1)
sd = 21 A1
3
(b)50.619
(17 × 53 + 25 × 49)/42 (M1)
50.619 A1
2
Question 2Structured · 5 marksA* challenge

For a set of 20 test scores, the lower quartile is 24, the median is 34, the upper quartile is 37 and the largest score is 62. The mean score is 34.5.

(a)

Find the interquartile range.

[1]
(b)

Show that the score of 62 is an outlier.

[2]
(c)

The outlier is removed. Find the new mean.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)13
13 A1
1
(b)62 > 56.5
37 + 1.5 × 13 = 56.5 M1
62 > 56.5 so it is an outlier R1
2
(c)33.053
(20 × 34.5 − 62)/19 (M1)
33.053 A1
2
Question 3Structured · 5 marks

The number of books read by a group of students last month is shown.

Books012345
Frequency58710610
Table 3.1
(a)

Find the mean and the standard deviation of the number of books read.

[3]
(b)

Find the median.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)mean 2.74, sd 1.66
GDC with frequencies (M1)
mean 2.74 A1
sd 1.66 A1
3
(b)3
46 values, median position 23.5 (M1)
3 A1
2
Question 4Structured · 3 marks

The table shows the time, t minutes, spent by customers in a shop.

t0–1010–2020–3030–4040–50
Frequency4512105
Table 4.1
(a)

Write down the modal class.

[1]
(b)

Find an estimate of the mean time.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)20–30
20 ≤ t < 30 A1
1
(b)26.9
mid-interval values (M1)
26.9 A1
2
Question 5Structured · 5 marksA* challenge

The table shows the scores of 25 students. The mean score is 3.16.

Score12345
Frequency4p5q4
Table 5.1

Find the values of p and q.

[5]
Show answers and mark scheme
PartAnswer and marking pointsMarks
p = 4, q = 8
p + q = 12 A1
Σfx: 4 + 2p + 15 + 4q + 20 = 79 A1
solving simultaneously (M1)
p = 4 A1
q = 8 A1
5
Question 6Structured · 5 marksA* challenge

A set of 18 marks has mean 42 and standard deviation 8.

(a)

Each mark is multiplied by 2 and then 5 is subtracted. Find the new mean and standard deviation.

[3]
(b)

A second group of 21 students has a mean mark of 45 on the original test. Find the mean mark of all 39 students.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)mean 79, sd 16
mean = 2 × 42 − 5 = 79 A1
adding does not change the sd (M1)
sd = 16 A1
3
(b)43.615
(18 × 42 + 21 × 45)/39 (M1)
43.615 A1
2

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Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in