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.
$38, 70, 48, 34, 63, 42, 55, 44, 53, 47$

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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