Download Exercise 16E

16
Measures of Dispersion
Name :
16E
Date :
Mark :
Multiple Choice Questions
1.
Find the range of the group of numbers
-10, -8, 1, 11, 19.
A. I only
B.
II only
A. 1
C.
II and III only
B. 2.6
D. I, II and III
C. 24
D. 29
2.
4.
D
B.
42
C.
46.5
D. 48.5
3.
Which of the following sets of data has
the largest inter-quartile range?
A. -4, 18, 32, 6
If the inter-quartile range of the group of
numbers 0, 3, 7, 17, 30, x, 51, 70 is 41.5,
find the value of x. (Assume the group of
numbers are arranged in ascending
order.)
A. 41.5
B.
0, 10, -27, 3, -15
C.
-1, -11, -31, -101, -71, -61
D. 5, 53, 47, 21, 1
5.
Number of siblings
Frequency
0
3
1
10
2
8
3
5
4
2
Given the heights (in cm) of two groups
of students:
Group A: 131 cm, 150 cm, 147 cm,
138 cm, 144 cm
Group B: 139 cm, 148 cm, 132 cm,
151 cm, 140 cm
I.
The ranges of the heights of the two
groups of students are the same.
II.
The means of the heights of the two
groups of students are the same.
III. The inter-quartile ranges of the
heights of the two groups of
students are the same.
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C
The table below shows the number of
siblings of a class of students.
B
Which of the following is / are the true?
D
Find the median and the inter-quartile
range of the number of siblings of the
students.
Median
Inter-quartile range
A.
1.5
1.5
B.
2
1.5
C.
2
2
D.
4
28
B
16
6.
III. Inter-quartile range of A < interquartile range of B
The figure shows the cumulative
frequency polygon of the heights of 20
plants.
A. I and II only
Heights of 20 plants
Cumulative frequency
20
B.
I and III only
C.
II and III only
D. I, II and III
A
15
8.
10
2
4
6
8
10
12
14
5
Find the inter-quartile range of the
heights of the plants.
The above box-and-whisker diagram
show the distribution of a set of data.
Find the range, median and inter-quartile
range of the set of data.
Range Median Inter-quartile
range
A. 1.2 cm
A.
5
8.5
2.5
B.
2.1 cm
B.
5
9
11
C.
2.5 cm
C.
10
9
5
D.
10
6
11
0
1
2
3
4
5
Height (cm)
D. 3.7 cm
C
The following are the cumulative
frequency polygons of two sets of data.
9.
C
Company A
Company B
200
Cumulative frequency
7.
Measures of Dispersion
Salary ($)
6 000 7 000 8 000 9 000 10 000 11 000
150
The above box-and-whisker diagrams
show the salaries distributions of two
companies. Which of the following
measures are the same for these two
companies?
Data set A
100
Data set B
50
0
20
40
60
80
Which of the following is / are true?
I.
Range of A > range of B
II.
Median of A < median of B
100
A. Range
B.
Median
C.
Lower quartile
D. Inter-quartile range
B
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Data handling
10.
12.
Test 1
Chinese
English
Test 2
Mathematics
Mark
0
20
40
60
80
100
Mark
The above box-and-whisker diagrams
show the marks distributions of two tests
in a class. Which of the following is / are
true?
I.
Median of test 1 < median of test 2
II.
Range of test 1 > range of test 2
A. II only
III only
C.
I and II only
60
70
80
90
100
The above box-and-whisker diagrams
show the marks distributions of three
examinations in a class. If a student gets
65 marks in all three subjects, in which
subject does he perform the best?
B.
English
C.
Mathematics
D. Chinese and English
D. II and III only
11.
50
A. Chinese
III. Inter-quartile range of test 1 =
Inter-quartile range of test 2
B.
40
D
Bank A
Bank B
A
13. It is given that the range, the median and
the inter-quartile range of a set of data
are 9, -11 and 6 respectively. Which of
the following box-and-whisker diagrams
may represent the distribution of the set
of data?
A.
Bank C
-16 -14 -12 -10
Deposits ($)
0
5 000
25 000
15 000
10 000
20 000
C.
Bank A and bank C
D. Bank B and bank C
-4
-15 -14 -13 -12 -11 -10
-9
-21 -19 -17 -15 -13 -11
-9
-13 -11
-1
C.
A. Bank A
Bank B
-6
B.
The above box-and-whisker diagrams
show the deposits distribution of three
banks. Which bank(s) has / have the
largest inter-quartile range?
B.
-8
D.
C
-9
-7
-5
-3
D
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16
14. The following table shows the frequency
distribution of the weights of a group of
cats.
Weight x (kg)
Frequency
0£x<2
5
2£x<4
8
4£x<6
2
6£x<8
4
8 £ x < 10
1
8
C.
y + 3.16
10
B.
Weight (kg)
0
2
4
6
8
10
C.
Weight (kg)
0
2
4
6
8
10
0
2
4
6
8
10
A
A
Cumulative frequency
6
3.53
17. The following figures show the
cumulative frequency curves of three
sets of data. Which data set has the
largest and the smallest standard
deviations?
Weight (kg)
4
B.
D. y + 3.53
A.
2
16. Find the standard deviation of the set of
data y + 1, y + 2, y + 5, y + 9, y + 8
correct to 3 significant figures.
A. 3.16
Which of the following box-and-whisker
diagrams may represent the distribution
of the weights of the group of cats?
0
Measures of Dispersion
B
C
Largest
Smallest
A.
A
B
B.
A
C
C.
C
A
D.
C
B
C
D.
Weight (kg)
A
15. Find the standard deviation of the set of
data 2, -17, -5, 0, 9, 11.
A. 0
B.
9.31 (cor. to 3 sig. fig.)
C.
14
D. 86.7 (cor. to 3 sig. fig.)
B
191
Data handling
18. The following figure shows the
distribution of the number of credit cards
owned by a group of people.
Number of credit cards
owned by a group of people
III. Standard deviation of class A >
standard deviation of class B
A. I only
B.
III only
C.
I and II only
D. II and III only
C
Frequency
15
20. Given three sets of data below. Arrange
them in descending order of standard
deviations.
10
5
0
1
2
3
4
50, 71, 38, 56, 60, 45
II.
b + 17, b - 20, b + 6, b - 4, b + 5, b
III. -2d, -2d + 1, -2d - 28, -2d - 9,
-2d
Number of credits cards
Find the standard deviation of the
number of credit cards owned by the
group of people.
A. I, II, III
B.
I, III, II
A. 0.831 (cor. to 3 sig. fig.)
C.
II, I, III
B.
0.843 (cor. to 3 sig. fig.)
D. II, III, I
C.
2.37 (cor. to 3 sig. fig.)
D. 2.69 (cor. to 3 sig. fig.)
A
19. The following table shows the weights
distribution of school bags of students in
two classes.
Weight (kg)
Class A
Class B
2.1 - 3.0
4
7
3.1 - 4.0
12
10
4.1 - 5.0
10
9
5.1 - 6.0
6
6
Which of the following is / are true?
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I.
I.
Mean of class A > mean of class B
II.
Median of class A > median of class
B
D
21. If the mean and the standard deviation of
x1, x2, º , x7 are -6 and 4.3 respectively,
find the mean and the standard deviation
of x1 + 3, x2 + 3, º , x7 + 3.
Mean
Standard deviation
A.
-3
4.3
B.
-3
7.3
C.
-6
4.3
D.
-6
7.3
A
16
22. The inter-quartile range and the standard
deviation of a set of data are r and s
respectively. If each datum in the data
set is increased by 3%, what are the
inter-quartile range and the standard
deviation of the new set of data?
Inter-quartile
range
Standard
deviation
A.
0.97r
0.97s
B.
r
s
C.
1.03r
s
D.
1.03r
1.03s
D
23. If one datum is deleted from x - 3, x - 2,
x + 1, x + 4 and x + 5, the standard
deviation increases. Which of the
following should be the deleted datum?
25. Consider the following set of data:
1, 2, 3, 5, 7, 7, 10
If a datum ‘0’ is inserted in the set of
data, what are the effects on the range,
median and inter-quartile range of the set
of data?
InterStandard
Range
quartile
deviation
range
A. Increased
Increased
Increased
B. Increased
Decreased
Increased
C. Unchanged
Increased
Decreased
D. Unchanged
Decreased
Decreased
A
26. The following table shows the mean
salaries of employees of two companies
A. x - 3
B.
x-2
C.
x+1
Company
Mean Salary ($)
D. x + 5
C
24. The mean and the standard deviation of
the ages of a group of children are 7 and
1.31 respectively. If a child of age 7
joins the group of children, what are the
effects on the mean and the standard
deviation of the ages of the group of
children?
Mean
Standard deviation
Measures of Dispersion
A
B
8000
7000
If an employee having salary $7000 in
company B leaves the company and joins
company A with a new salary $8000,
what are the effects on the mean and the
standard deviation of the salaries of the
employees of companies A?
Mean
Standard deviation
A.
Increased
Increased
B.
Unchanged
Increased
A.
Unchanged
Increased
C.
Unchanged
Decreased
B.
Unchanged
Decreased
D.
Decreased
Unchanged
C.
Increased
Increased
D.
Decreased
Decreased
C
B
193