Question

Mean deviation of $6,8,12,15,10,9$ through mean is

• A. $10$
• B. $2.33$
• C. $2.5$
• D. None of these

Answer 1

The correct option is B

$2.33$

Explanation for the correct option:

Mean deviation of the data:

Given - The observations are $6,8,12,15,10,9$

Let the mean of the given observations is $\overline{x}$

By applying the formula of mean

$$\begin{gathered} \overline{\mathbf{x}}\mathbf{=}\frac{\mathbf{sum}\mathbf{}\mathbf{of}\mathbf{}\mathbf{observations}}{\mathbf{number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{observations}} \\ \Rightarrow \overline{x}=\frac{\left\{6+8+12+15+10+9\right\}}{6} \\ \Rightarrow \overline{x}=\frac{60}{6} \\ \Rightarrow \overline{x}=10 \end{gathered}$$

By applying the formula of mean deviation

$$\begin{gathered} \mathit{M}\mathbf{.}\mathit{D}\mathbf{=}\frac{\mathbf{\sum }_{}^{}\left|x_i-\overline{x}\right|}{{\mathbf{N}}_{\mathbf{t}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}}} \\ M.D=\frac{\left|6-10\right|+\left|8-10\right|+\left|12-10\right|+\left|15-10\right|+\left|10-10\right|+\left|9-10\right|}{6} \end{gathered}$$

Applying modulus to each term

$$\begin{gathered} M.D=\frac{4+2+2+5+0+1}{6} \\ M.D=\frac{14}{6} \\ M.D=2.33 \end{gathered}$$

Hence, the correct option is (B)