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.
• B. -
• C.
• D. -
  

Answer 1

The correct option is B

-

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

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

Which would be ${\sum }_{i=1}^n$ $f_i|$ $x_i$ - $\overline{x}$$|$

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

$\therefore$ Mean deviation about mean = $\frac{1}{N}$${\sum }_{i=1}^n$ $f_i|$ $x_i$ - $\overline{x}$$|$

$\therefore$ option b