Question

The mean deviation of the data 2, 9, 9, 3, 6, 9, 4 from the mean is
(a) 2.23
(b) 2.57
(c) 3.23
(d) 3.57

Answer 1

Given data is 2, 9, 9, 3, 6, 9, 4
By arranging the observations in ascending order of magnitude,
We obtain 2, 3, 4, 6, 9, 9, 9
Mean of given observations

$\begin{array}{rcl}\overline{X}& =& \frac{2+3+4+6+9+9+9}{7}\\ & =& \frac{42}{7}\\ \overline{X}& =& 6\end{array}$

xi	$\left|d_i\right|=\left|x_{\mathit{i}}-\overline{x}\right|=\left|x_{\mathit{i}}-6\right|$
2 3 4 6 9 9 9 Total	4 3 2 0 3 3 3 $\sum _{}{d}_i=18$

$$\begin{gathered} \mathrm{Then}\mathrm{Mean}\mathrm{deviation}\mathrm{is}\frac{1}{x}\sum _{}\left|d_i\right| \\ =\frac{1}{7}\times 18 \end{gathered}$$
i.e Mean deviation = 2.57

Hence, the correct answer is option B.