4 Measures of Dispersion
2.
Since the measures of central tendency for the two athletes
are all the same, they performed equally well.
3.
From the dot-plots, we observe that the scores of athlete
A
are more spread out.
Hence, the performance of athlete
B
is more stable.
Activity 4.2 (p. 4.27)
1.
(a)
Set
A
Set
B
Range
9
9
Inter-quartile range
5
5
(b)
No
2.
No. By inspection, set
A
is more dispersed.
Activity 4.3 (p. 4.40)
1.
English
2.
(a)
6
(b)
5
3.
No. We don’t know the distributions of the marks./ We
don’t know how many students got higher marks than
Mary in each subject. (or any other reasonable answers)
4.
The dispersion of the marks of the class in each subject.
Activity 4.4 (p. 4.53)
1.
Measure of
dispersion
Data set
A
Data set
B
Data set
C
Range
3
3
6
Inter-quartile
range
1.5
1.5
3
Standard
deviation
1
1
2
2.
The measures of dispersion of data set
B
are the same as
those of data set
A
.
3.
The measures of dispersion of data set
C
are twice those of
data set
A
.
Let’s
Discuss
Let’s Discuss (p. 4.30)
No, the result of their suggested formula is always zero.
Let’s Discuss (p. 4.55)
(a)
40, 90 (or any other reasonable answers)
(b)
65, 66 (or any other reasonable answers)
Classwork
Classwork (p. 4.12)
Data
Lower half of
the data
Upper half of
the data
(a)
2, 5, 6, 8, 12, 13
2, 5, 6
8, 12, 13
(b)
1, 5, 7, 9, 11, 14,
15
1, 5, 7
11, 14, 15
(c)
3,
1, 0, 2, 2,
4, 6, 7
3,
1, 0, 2
2, 4, 6, 7
(d)
18, 30, 10, 34,
45, 18, 24, 8, 28
8, 10, 18, 18
28, 30, 34, 45
(e)
4,
4,
1, 0,
1, 0,