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.
$\overline{\text{x}}=\frac{34+66+30+38+44+50+40+60+42+51}{10}=45.5$
$\text{MD}=\frac{1}{\text{n}}\sum_\limits{\text{i}=1}^\text{n}|\text{d}_\text{i}|,\text{where}|\text{d}_\text{i}|=|\text{x}_\text{i}-\overline{\text{x}}|$
$x_i$
$|d_i| = |x_i - 45.5|$
$34$
$11.5$
$66$
$20.5$
$30$
$15.5$
$38$
$7.5$
$44$
$1.5$
$50$
$4.5$
$40$
$5.5$
$60$
$14.5$
$42$
$3.5$
$51$
$5.5$
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.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free