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.
$22, 24, 30, 27, 29, 31, 25, 28, 41, 42$

Answer

Let $\overline{\text{x}}$ be the mean of the data set.
$\overline{\text{x}}=\frac{22+24+30+27+29+31+25+28+41+42}{10}=29.9=$
$x_i$
$|d_i| = |x_i - 29.9|$
$22$
$7.9$
$24$
$5.9$
$30$
$0.1$
$27$
$2.9$
$29$
$0.9$
$31$
$1.1$
$25$
$4.9$
$28$
$1.9$
$41$
$11.9$
$42$
$12.1$
Total
$48.8$
$\text{MD}=\frac{1}{10}\times48.8=4.88$
$\overline{\text{x}} - M.D. = 29.9 - 4.88 = 25.02,$
and, $\overline{\text{x}} + M.D. = 29.9 + 4.88 = 34.78$
There are $5$ observation between $25.02$ and $34.78.$

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