Junior Secondary · Mathematics

Measure of Central Tendency: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Measure of Central Tendency.

10 questions25 marksFree, no account

Question 1

1 mark

Find the median of the following set of scores: \(12, 7, 10, 8, 14\).

Question 2

1 mark

The mean of five consecutive even integers is \(M\). What is the value of the smallest of these five integers in terms of \(M\)?

Question 3

1 mark

The estimated mean of the following grouped frequency distribution is \(27\). Find the missing frequency \(k\):

Class Interval | Frequency
\(10 - 19\) | \(4\)
\(20 - 29\) | \(k\)
\(30 - 39\) | \(6\)
\(40 - 49\) | \(2\)

Question 4

1 mark

The mean of a data set is \(45\). If each value in the data set is multiplied by \(3\), what is the new mean?

Question 5

1 mark

The following table shows the scores of \(40\) students in a quiz:

Score | 0 | 1 | 2 | 3 | 4 | 5
Frequency | 3 | 7 | 12 | 8 | 5 | 5

Find the median score of the students.

Question 6

3 marks

The heights of five students are measured as \(148\) cm, \(152\) cm, \(145\) cm, \(155\) cm, and \(h\) cm. If their mean height is \(150\) cm, find the value of \(h\).

Write your answer out first, then check it against the worked solution.

Question 7

4 marks

A set of five distinct positive integers has a mean of \(20\) and a median of \(18\). If the mode does not exist and the largest integer in the set is \(32\), find the maximum possible value of the second largest integer.

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Question 8

5 marks

The table below shows the frequency distribution of the weights of \(30\) packages.

Weight (kg) | Frequency
\(0 - 10\) | \(4\)
\(10 - 20\) | \(a\)
\(20 - 30\) | \(b\)
\(30 - 40\) | \(6\)

If the estimated mean weight of the packages, calculated using class marks, is exactly \(22\text{ kg}\), find the values of \(a\) and \(b\).

Write your answer out first, then check it against the worked solution.

Question 9

3 marks

A group of 8 students recorded the number of books they read during the summer holidays:

\(8, 4, 7, 10, 4, 9, 7, 7\)

(a) Find the mean of the number of books read.

(b) Find the mode of the data set.

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Question 10

5 marks

A student's final grade in a mathematics course is calculated using a weighted mean. The weights for three components are as follows:

Homework: 20%
Mid-term Exam: 30%
Final Exam: 50%

In the first semester, Kelvin scored 90 in Homework and 70 in the Mid-term Exam.

(a) If Kelvin scores 82 in the Final Exam, calculate his overall weighted mean score.

(b) If Kelvin wants to achieve an overall weighted mean score of at least 85, find the minimum score he must obtain in the Final Exam.

Write your answer out first, then check it against the worked solution.

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