Question

Find the mean deviation about the mean for the following data:

15, 17, 10, 13, 7, 18, 9, 6, 14, 11

Answer 1

Let the mean of the given data be $\overline{x}$. Then,

$\overline{x}=\frac{{\sum }_{i=1}^n{x}_i}{n}=\frac{120}{10}=12[\because n=10]$

The values of $(x_i-\overline{x})$ are:

$3,5,-2,1,-5,6,-3,-6,2,-1$

So, the values of $|x_i-\overline{x}|$ are:

$3,5,2,1,5,6,3,6,2,1$

$\therefore MD\left(\overline{x}\right)=\frac{{\sum }_{i=1}^n|x_i-\overline{x}|}{n}=\frac{34}{10}=3.4$

Hence, MD $\left(\overline{x}\right)$ = 3.4