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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 $\small 9$ $\small 13$ $\small 26$ $\small 30$ $\small 12$ $\small 10$

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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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