Question

The mid - points of class intervals $x_i$ along with respective frequencies $f_i$ for recorded observations are given. Calculate the mean deviations about mean $x$

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

Answer 1

The correct option is A

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

While calculating the mean of continuous frequency distributions we make assumption that frequency in each class is centered at its midpoint.

In a continuous frequency distribution once the mid points of class intervals are calculated the rest is same as for a discrete frequency distribution.

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

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

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