Find the numberof observation lying between X -M.D. and X + M.D. … - Vidyadip

Question

Find the numberof observation lying between $\overline{\text{X}}-\text{M.D. }$ and $\overline{\text{X}} +\text{ M.D.}$ is the mean deviation from the mean. $38, 70, 48, 34, 63, 42, 55, 44, 53, 47$

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Answer

Let $\overline{\text{x}}$ be the mean of the data set. $\overline{\text{x}}=\frac{38+70+48+34+63+42+55+44+53+47}{10}=49.4$

$x_i$	$\|d_i\| = \|x_i - 49.4\|$
38	11.4
70	20.6
48	1.4
34	15.4
63	13.6
42	7.4
55	5.6
44	5.4
53	3.6
47	2.4
Total	86.8

$\text{MD}=\frac{1}{10}\times86.8=8.68$ $\overline{\text{x}}$ - M.D. = 49.4 - 8.68 = 40.72 and, $\overline{\text{x}}$ + M.D. = 49.4 + 8.68 =58.08 There are 6 observation between 40.72 and 58.08.

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