Question

Given the population 10 top scores of Cricketer Saeed Anwer from February 1997 to June 2001

runs

108

104

95

103

63

72

105

90

88

77

a. Find the population variance and standard deviation of this set of data.

b. What would be the Saeed Anwar scour on 27th percentile and 1st quartile in above scores?

c. A sample is taken from the population 108, 101, 104, 63, 72

Find the sample variance and standard deviation.

Answer 1

(a)

(i)

Population Mean () is given by:

x	(x - )	(x - )2
108	17.5	306.25
104	13.5	182.25
95	4.5	20.25
103	12.5	156.25
63	-27.5	756.25
72	-18.5	342.25
105	14.5	210.25
90	-0.5	0.25
88	-2.5	6.25
77	-13.5	182.25
Total =		2162.5

Population Variance () is given by:

(ii)

Population Standard Deviation () is given by:

(b)

(i)

Arranging numbers in ascending order, we get:

63,72,77,88,90,95,103,104,105,108

27th Percentile Position is given by:

Interpolating between 2nd & 3rd position values, i.e., 72 & 77, we get:

P27 = 72 + 0.97 X (77 - 72) = 76.85

So,

27th percentile = 76.85

(ii)

Arranging numbers in ascending order, we get:

63,72,77,88,90,95,103,104,105,108

1st Quartile = 25th Percentile Position is given by:

Interpolating between 2nd & 3rd position values, i.e., 72 & 77, we get:

P25= 72 + 0.75 X (77 - 72) = 75.75

So,

1st Quartile = 25th percentile = 75.75

(c)

(i)

Sample Mean () is given by:

x	x-	(x - )2
108	18.4	338.56
101	11.4	129.96
104	14.4	207.36
63	-26.6	707.56
72	-17.6	309.76
Total =		1693.2

Sample Variance (s2) is given by:

(ii)

Sample Standard Deviation (s) is given by: