Question

The mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from the mean is

(a) 2 (b) 2.57 (c) 3 (d) 3.57

Answer 1

The given observations are 3, 10, 10, 4, 7, 10, 5.

∴ Mean, $\overline{x}=\frac{3+10+10+4+7+10+5}{7}=\frac{49}{7}=7$

Now,

Mean deviation from mean, MD

$=\frac{\sum _{}\left|x_i-7\right|}{7}$

$$\begin{gathered} =\frac{\left|3-7\right|+\left|10-7\right|+\left|10-7\right|+\left|4-7\right|+\left|7-7\right|+\left|10-7\right|+\left|5-7\right|}{7} \\ =\frac{4+3+3+3+0+3+2}{7} \\ =\frac{18}{7} \\ =2.57 \end{gathered}$$

Hence, the correct answer is (b).