Question

The mean deviation from the mean of the set of observations $-1,0,4$ is

• A. $3$
• B. $1$
• C. $-2$
• D. $2$

Answer 1

The correct option is D

$2$

Explanation for the correct option:

Step 1: Find the mean of the given observations.

A set of observations $-1,0,4$ is given.

So, the mean $\overline{x}$ is given by:

$$\begin{gathered} \overline{x}=\frac{-1+0+4}{3} \\ \Rightarrow \overline{x}=1 \end{gathered}$$

Therefore, the mean of the given observations is $1$.

Step 2: Find the mean deviation.

The formula of mean deviation $\text{MD}$ is as follows:

$\text{MD}=\frac{{\displaystyle \sum _{i=1}^n}\left|x_i-\overline{x}\right|}{n}$

So, the mean deviation for the given observations is as follows:

$$\begin{gathered} \text{MD}=\frac{{\displaystyle \sum _{i=1}^3}\left|x_i-1\right|}{3} \\ \Rightarrow \text{MD}=\frac{{\displaystyle 2+1+3}}{3} \\ \Rightarrow \text{MD}=\frac{{\displaystyle 6}}{3} \\ \Rightarrow \text{MD}=2 \end{gathered}$$

Therefore, the mean derivation for the given observation is $2$.

Hence, option $D$ is the correct option.