Page 240 - DSOC404_METHODOLOGY_OF_SOCIAL_RESEARCH_ENGLISH

Methodology of Social Research

notes
Example 7 Use the following table to compute the standard deviation

Weight (in Pounds) Number of People
70–80 12

80–90 18
90–100 35
100–110 49
110–120 50

120–130 45
130–140 20
140–150 8

to solve this question using short-cut method, we will assume the centre–value of any of the class
intervals to be the mean.
+
Let us say 110 120 = 115 is the mean. Now we form the following table.
2

Weight (in number of Mid– Variation Variation of f × d = fd × d =
pounds) People point of of Mid– (d) Mid– fd fd 2
C.I. (f) Class– point from point from
intervals assumed assumed
x Mean Mean 115
(X – A) divided by
class width
(X–A/i)
70–80 12 75 –40 –4 –48 192
80–90 18 85 –30 –3 –54 162

90–100 35 95 –20 –2 –70 140
100–110 49 105 –10 –1 –49 49
110 –120 50 115 0 0 0 0
120–130 45 125 10 1 45 45
130 –140 20 135 20 2 40 80

140–150 8 145 30 3 24 72
N = 237 S fd = –112 Sfd = 740
2

formula—

S fd 2  S fd 2 740 − 112 2
σ = i N −   N   = 10 237   237  

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