Question

how mean,median,mode,docile,percentile r calculated from cumulitive frequency distributiion?

Answer 1

Mean:

$$\bar{x} = \frac{x_1 + x_2 + \dots + x_n}{n} = \frac{\sum x}{n} = \frac{1}{n} \sum x.$$

Median

$$Me = X_{Me} + i_M \frac{\frac{\sum f}{2} - S_{Me-1}}{f_{Me}}$$

Mode

$$Mo = X_{Mo} + i_{Mo} \frac{f_{Mo} - f_{Mo-1}}{(f_{Mo} - f_{Mo-1}) + (f_{Mo} - f_{Mo+1})}$$

Decile

$$D_k = L_i + \frac{\frac{k \cdot N}{10} - F_{i-1}}{f_i} \cdot a_i$$

Quartile

$$Q_k = L_i + \frac{\frac{k \cdot N}{4} - F_{i-1}}{f_i} \cdot a_i$$

$L_i$ is the lower limit of the quartile class.

$N$ is the sum of the absolute frequency.

$F_{i-1}$ is the absolute frequency immediately below the quartile class.

$a_i$ is the width of the class containing the quartile class.

The quartiles are independent of the widths of the classes.