Question

For the given distinct values $x_1,x_2,x_3,.....x_n$ occurring with frequencies $f_1,f_2,f_3,...f_n$ respectively. The mean deviation about mean where $\overline{x}$ is the mean and N is total number of observations would be

• A. $\frac{1}{N}\sum _{i=1}^n{f}_i|x_i-M|$
• B. $\frac{1}{N}\sum _{i=1}^n{f}_i|x_i-\overline{x}|$
• C. $\sum _{i=1}^n\frac{|x_i-\overline{x}|}{N}$
• D. $N\cdot f_i\sum _{i=1}^n|x_i-\overline{x}|$

Answer 1

The correct option is B

$\frac{1}{N}\sum _{i=1}^n{f}_i|x_i-\overline{x}|$

Clearly mean of the given distribution will be
$x=\sum _{i=1}^n\frac{f_i{x}_i}{\sum _{i=1}^n{f}_i}$

To find the mean deviation about $\overline{x}$ we need sum of absolute deviation about $\overline{x}$ for each $x_i$

Which would be ${\sum }_{i=1}^n{f}_i\left(x_i-x\right|$

Total number of observations = $\sum _{i=1}^n{f}_i=N$

$\therefore$ Mean deviation about mean = $=\frac{1}{N}{\sum }_{i=1}^n{f}_i\left(x_i-x\right|$

$\therefore$ option b