Question

Calculate the mean for the following data using step deviation method:

Class interval (X)	0-10	10-20	20-30	30-40	40-50	50-60	60-70
Frequency	15	10	15	20	25	30	35

Round off your answer to the nearest whole number.

• A. $41$
• B. $42$
• C. $43$
• D. $44$

Answer 1

Answer: (B)

$42$

Consider the following table, to calculate mean by "step deviation method":

$x_i$=mid value of class interval

Assumed mean $a=35$

class interval $c=10$

$ci$	$f_i$	$x_i$	$u_i=\frac{x_i-a}{c}$	$f_i{u}_i$
$0-10$	$15$	$5$	$-3$	$-45$
$10-20$	$10$	$15$	$-2$	$-20$
$20-30$	$15$	$25$	$-1$	$-15$
$30-40$	$20$	$35$	$0$	$0$
$40-50$	$25$	$45$	$1$	$25$
$50-60$	$30$	$55$	$2$	$60$
$60-70$	$35$	$65$	$3$	$105$

$N=\Sigma f_i=150$

$\Sigma f_i{u}_i=110$

Mean $\overline{x}=a+\frac{\Sigma f_i{u}_i}{N}\times c$

$\therefore \overline{x}=35+\frac{110}{150}\times 10=42.3334\approx 42$

Hence, option $B$ is correct.