Mathematics Chapter Quiz
Ch.5 Measures of Central Tendency and Other Statistical Values
Name: ________________________
1.
Class: ________(
)
Date: ________
The following data shows the monthly salaries of 6 staffs in a company.
$15000, $15000, $16000, $18000, $24000, $77000
(a) The boss of the company claims that the average salary of his staff is $27500. How can the
boss come to this conclusion? (You need not show the calculation steps.)
(b) Do you think the boss’s claim reasonable? Explain you answer. If your answer is ‘no’,
suggest a better way to show the average salary of the staffs.
(3 marks)
2.
The following tables show the cumulative frequency table and the frequency distribution table
of the amount (in $) spent by some students to buy gifts for a Christmas party respectively.
(a) Complete the tables.
Amount less than ($)
9.5
29.5
49.5
Cumulative Frequency
Amount ($)
69.5
9
10 − 29
30 − 49
50 − 69
70 − 89
89.5
109.5
23
30
90 − 109
Class Mark($)
Frequency
2
5
(b) Estimate the mean amount spent by students.
(5 marks)
1
3.
The stem-and-leaf diagram below shows the distribution of the weights (in kg) of a group of
members of a football team.
It is given that the median and the mode of the weights of the team are 56 kg and 58 kg
respectively.
(a) (i) Write down the values of a and b .
(ii) Hence, write down the mean weight of the group.
(3 marks)
(b) As the lightest and the heaviest members leave the team, four new members join the
football team. It is known that the mean weight of the members of the team remains
unchanged.
(i) Find the mean weight of the four new members.
(ii) Furthermore, it is given that the weights of two of the new members are 57 kg. Is it
possible that the median of the weight of the members remains unchanged? Explain
your answer.
(5 marks)
2
3
4.
The bar chart below shows the distribution of the ages of 46 children in a group. It is given
that the median of the ages of the children in the group is 7.5 .
(a) Find a and b .
(4 marks)
(b) Four more children with ages in the range 6 − 10 now join the group. It is known that the
mode of the ages of the children becomes 8 after the joining of the children. Find the
greatest and the least possible mean after the joining of the children.
4
(4 marks)
5
For Question 5 – 10, write down the choice in the boxes provided; otherwise no marks will be
given, each question carries 1 mark.
5.
6.
7.
The graph below shows the cumulative frequency curve of the time (in min) spent by students to
complete a task. Find the median time spent by students to complete the task.
A.
27.0 minutes
B.
27.5 minutes
C.
28.0 minutes
D.
28.5 minutes
In a company, the mean age of 10 male staff and 6 female staff is 30.5. If the mean age of the
male staff is 35.3, then the mean age of the female staff is
A.
22.5.
B.
25.7.
C.
27.6.
D.
28.2.
When a number is deleted from the data set 2, 3, 3, 6, 8, 11, 11, 12, 13, the mean will decrease
and the median will increase. The deleted number is
A.
6.
B.
8.
C.
11.
D.
13.
6
8.
The following table shows the test marks of Sandy in 5 tests.
Marks
59
64
69
74
80
Weight
3
x
3
2
1
If the weighted mean mark of Sandy in these 5 tests is 67, find the value of x.
9.
A.
1
B.
2
C.
3
D.
4
Consider the following set of data.
x – 1,
x,
x + 1,
x + 2,
x+3
If 3 is first added to each datum in the set, and each of the result is multiplied by 2, what is the
new mean of the new set of data?
A.
x+3
B.
x+4
C.
2x + 6
D.
2x + 8
10. If the mode and the median of the ten numbers 2, 4, 0, 3, 6, 1, 7, 9, a and b are 7 and 4.5
respectively, then the mean of these ten numbers is
A.
4.3.
B.
4.4.
C.
4.5.
D.
4.6.
5
6
7
8
-- END OF PAPER -7
9
10