IB · Mathematics: Analysis & Approaches SL & HL · Statistics & probability

Descriptive statistics: IB Mathematics: Analysis & Approaches questions with answers

Free Descriptive statistics questions for IB Mathematics: Analysis & Approaches (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 · 6 marksA* challenge

The data set {7, 5, 7, a, b} has mean 6 and variance 285, where a < b.

Find the values of a and b.

[6]
Show answers and mark scheme
PartAnswer and marking pointsMarks
a = 2, b = 9
a + b = 11 A1
use of variance = Σx2n − x̄2 M1
a2 + b2 = 85 A1
substituting b = 11 − a M1
a2 − 11a + 18 = 0 A1
a = 2, b = 9 A1
6
Question 2Structured · 4 marks

For a data set, the lower quartile is 14 and the upper quartile is 25.

Determine the values below which and above which a data value would be considered an outlier.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
below −2.5, above 41.5
IQR = 11 A1
1.5 × IQR M1
lower −2.5 A1
upper 41.5 A1
4
Question 3Structured · 4 marks

For a set of test scores, the lower quartile is 19, the median is 25 and the upper quartile is 33. The smallest score is 12 and the largest score is 56.

(a)

Find the interquartile range.

[1]
(b)

Determine whether the largest score is an outlier. Justify your answer.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)14
14 A1
1
(b)yes, an outlier
upper boundary Q3 + 1.5 × IQR (M1)
= 54 A1
56 > 54, so it is an outlier R1
3
Question 4Structured · 5 marks

A data set of 10 values has mean 29 and standard deviation 2.4.

(a)

One further value, x, is added to the data set and the mean becomes 30. Find x.

[3]
(b)

Each of the original 10 values is multiplied by 5 and then has 6 subtracted. Write down the new mean and the new standard deviation.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)40
total of original values = 290 (A1)
290 + x11 = 30 (M1)
x = 40 A1
3
(b)mean 139, sd 12
mean 139 A1
standard deviation 12 (unaffected by adding a constant) A1
2
Question 5Structured · 4 marks

The ages of 8 people are
33, 24, 21, 17, 39, 16, 34, 15

(a)

Find the mean and the standard deviation.

[2]
(b)

Each person’s age is increased by 5 years. Write down the new mean and standard deviation.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)24.9; 8.68
mean 24.9 A1
sd 8.68 A1
2
(b)29.9; 8.68
mean 29.9 A1
sd unchanged A1
2
Question 6Structured · 6 marksA* challenge

The data set {2, 4, 9, a, b} has mean 6 and variance 745, where a < b.

Find the values of a and b.

[6]
Show answers and mark scheme
PartAnswer and marking pointsMarks
a = 3, b = 12
a + b = 15 A1
use of variance = Σx2n − x̄2 M1
a2 + b2 = 153 A1
substituting b = 15 − a M1
a2 − 15a + 36 = 0 A1
a = 3, b = 12 A1
6

More Statistics & probability questions

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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