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Measures of Central Tendency and Dispersion — Paper 2 Multiple-Choice Questions

Eight multiple-choice questions in the style of Paper 2: averages from tables and lists, weighted and grouped means, standard scores, and what happens to the mean, median and standard deviation when data are transformed or added. Answers are on the page. Detailed solutions can be requested by email.

8 questions · about 12 minutes · answers below each question

All questions are original, written for Math and AI Academy and modelled on past-paper style. They are not reproductions of HKEAA examination questions.

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Question 1 — unknown data from the mean; which statistics must hold whatever the unknowns are
Question 2 — mean, median and mode from a frequency table
Question 3 — weighted mean with an inequality
Question 4 — estimating the mean of grouped data with class marks
Question 5 — standard deviation from one standard score, then a score from another
Question 6 — mean and standard deviation from two (score, standard score) pairs
Question 7 — standard deviation after multiplying by a negative number and adding a constant
Question 8 — adding a datum equal to the mean: what changes and what must not

Question 1 · Modelled on 2017 P2 Q30

Consider the following positive integers:

34468911 m n

If the mean of the above positive integers is

6

, which of the following must be true?

I. The median of the above positive integers does not exceed $6$ .
II. The range of the above positive integers is at least $8$ .
III. The mode of the above positive integers is $4$ .

I and II only
I and III only
II and III only
I, II and III

Show answer

A. I and II only

Detailed solutions can be requested by email.

Question 2 · Modelled on 2020 P1 Q9

The table below shows the numbers of goals scored by a football team in 20 matches.

Number of goals Number of matches 0316253442

Find the mean, the median and the mode of the distribution.

mean $= 1.8$ , median $= 1.5$ , mode $= 1$
mean $= 2$ , median $= 2$ , mode $= 1$
mean $= 1.8$ , median $= 2$ , mode $= 6$
mean $= 1.8$ , median $= 2$ , mode $= 1$

Show answer

D. mean $= 1.8$ , median $= 2$ , mode $= 1$

Detailed solutions can be requested by email.

Question 3 · New sub-type: weighted mean

The overall score of a student is the weighted mean of the coursework score and the examination score, with weights

40%

and

60%

respectively. Mary scores

65

marks in the coursework. If her overall score is at least

71

marks, her least possible examination score is

$71$ marks.
$75$ marks.
$77$ marks.
$80$ marks.

Show answer

B. $75$ marks

Detailed solutions can be requested by email.

Question 4 · New sub-type: mean of grouped data

The table below shows the distribution of the weights of 20 students.

Weight (kg) Frequency 40 - 44 2 45 - 49 8 50 - 54 6 55 - 59 4

Estimate the mean weight of the students.

$47.5 kg$
$48 kg$
$50 kg$
$52 kg$

Show answer

C. $50 kg$

Detailed solutions can be requested by email.

Question 5 · Modelled on 2021 P2 Q44

In an examination, the mean of the scores is

52

marks. A boy scores

40

marks and his standard score is

- 1.5

. If the standard score of a girl in the examination is

2

, then her score is

$56$ marks.
$60$ marks.
$64$ marks.
$68$ marks.

Show answer

D. $68$ marks

Detailed solutions can be requested by email.

Question 6 · Modelled on 2023 P2 Q44

The table below shows the scores (in marks) and the corresponding standard scores of three students in a test.

Score (marks) Standard score 51 - 1.5 69 0.75 x 2

Find

x

$79$
$81$
$83$
$87$

Show answer

A. $79$

Detailed solutions can be requested by email.

Question 7 · Modelled on 2024 P2 Q45

If the variance of the six numbers

x_{1}, x_{2}, x_{3}, x_{4}, x_{5}

and

x_{6}

9

, then the standard deviation of the six numbers

2 - 4 x_{1}, 2 - 4 x_{2}, 2 - 4 x_{3}, 2 - 4 x_{4}, 2 - 4 x_{5}

and

2 - 4 x_{6}

$10$ .
$12$ .
$34$ .
$144$ .

Show answer

B. $12$

Detailed solutions can be requested by email.

Question 8 · Modelled on 2025 P2 Q45

The mean, the median and the standard deviation of nine numbers are

20

18

and

4

respectively. The number

20

is added to these nine numbers. Which of the following must be true?

I. The mean of the ten numbers is $20$ .
II. The median of the ten numbers is $18$ .
III. The standard deviation of the ten numbers is less than $4$ .

I only
I and II only
I and III only
II and III only

Show answer

C. I and III only

Detailed solutions can be requested by email.

Continue practising this topic: Try the Paper 2 Challenge MC for harder variants, or move to Paper 1 long questions — also available as Paper 1 Challenge.

Where this sits in the syllabus

Statistics questions usually close both sections of Paper 2: one in Section A on reading averages from data, and one or two at the very end of Section B on standard scores and on how the mean, median and standard deviation respond when data change. Quartiles and box-and-whisker diagrams belong to More about Statistics and are not tested here.

Full coverage of this topic, and the rest of the course, is on the Mathematics page. More sets are listed on the practice index.

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