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. 34, 66, 30, 38, 44, 50, 40, 60, 42, 51

Answer

Let $\overline{\text{x}}$ be the mean of the data set. $\overline{\text{x}}=\frac{34+66+30+38+44+50+40+60+42+51}{10}=45.5$ $\text{MD}=\frac{1}{\text{n}}\sum_\limits{\text{i}=1}^\text{n}|\text{d}_\text{i}|,\text{where}|\text{d}_\text{i}|=|\text{x}_\text{i}-\overline{\text{x}}|$
$\text{x}_i$ $\left|\mathrm{d}_{\mathrm{i}}\right|=\left|\mathrm{x}_{\mathrm{i}}-45.5\right|$
34
11.5
66
20.5
30
15.5
38
7.5
44
1.5
50
4.5
40
5.5
60
14.5
42
3.5
51
5.5
Total
90
$\text{MD}=\frac{1}{10}\times90=9$ $\overline{\text{x}}$ - M.D. = 45.5 - 9 = 36.5 Also, $\overline{\text{x}}$ + M.D. = 45.5 + 9 = 54.5 Hence, there are 6 observations between 36.5 and 54.5.

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