Question

For the given distinct values x₁, x₂, x₃ .....x_n occurring with frequencies f₁, f₂, f₃, ... f_n respectively. The mean deviation about mean would be

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Clearly mean of the given distribution will be $\overline{x}$ = $lim{\sum }_{i=1}^n$ = $\frac{fixi}{lim{\sum }_{i=1}^{n}fi}$

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

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

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

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

$\therefore$option b