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  • Find the mean deviation about the mean for the data. (2) 38, 70, 48, 40, 42, 55, 63, 46, 54, 44

2. Find the mean deviation about the mean for the data.

   \small 38,70,48,40,42,55,63,46,54,44

Answers (1)

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Mean (\overline{x}) of the given data:

\\ \overline{x} = \frac{1}{8}\sum_{i=1}^{8}x_i = \frac{38+70+48+40+42+55+63+46+54+44}{10} \\ = \frac{500}{10} = 50

The respective absolute values of the deviations from mean, |x_i - \overline{x}| are

12, 20, 2, 10, 8, 5, 13, 4, 4, 6

\therefore  \sum_{i=1}^{8}|x_i - 50| = 84

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

= \frac{84}{10} = 8.4

Hence, the mean deviation about the mean is 8.4.

Posted by

HARSH KANKARIA

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