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Find the mean deviation about the mean (10)

10. Find the mean deviation about the mean.

Height in cms \small 95-105 \small 105-115 \small 115-125 \small 125-135 \small 135-145 \small 145-155
Number of persond \small 9 \small 13 \small 26 \small 30 \small 12 \small 10

 

Answers (1)
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Height

in cms

Number of 

Persons f_i

Mid

Points x_i

f_ix_i |x_i - \overline{x}| f_i|x_i - \overline{x}|
95 -105 9 100 900 25.3 227.7
105 -115 13 110 1430 15.3 198.9
115-125 26 120 3120 5.3 137.8
125-135 30 130 3900 4.7 141
135-145 12 140 1680 14.7 176.4
145-155 10 150 1500 24.7 247
 

\sum{f_i}

=100

 

\sum f_ix_i

=12530

 

\sum f_i|x_i - \overline{x}|

=1128.8

 

N = \sum_{i=1}^{6}{f_i} = 100 ; \sum_{i=1}^{6}{f_ix_i} = 12530

\overline{x} = \frac{1}{N}\sum_{i=1}^{6}f_ix_i = \frac{12530}{100} = 125.3

Now, we calculate the absolute values of the deviations from mean, |x_i - \overline{x}|  and

\sum f_i|x_i - \overline{x}| = 1128.8

\therefore M.D.(\overline{x}) = \frac{1}{100}\sum_{i=1}^{6}f_i|x_i - \overline{x}|

= \frac{1128.8}{100} = 11.29

Hence, the mean deviation about the mean is 11.29

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