Question

Class interval	$4-8$	$8-12$	$12-16$	$16-20$
No. of employees	$5$	$10$	$15$	$20$

Find the mean of the following frequency distribution using step deviation method.

• A. $11$
• B. $12$
• C. $13$
• D. $14$

Answer 1

Answer: (D)

$14$

Answer:- By shortcut Method(Step deviation mean method)

Class interval width $\left(w\right)=8-4=4$

Class interval $\left(i\right)$	$X$	No. of employees $F$	$d=\frac{X-A}{i}$	$Fd$
$4-8$	$6$	$5$	-$1$	$-5$
$8-12$	$10=A$	$10$	$0$	$0$
$12-16$	$14$	$15$	$1$	$15$
$16-20$	$18$	$20$	$2$	$40$
		$\Sigma F=50$		$\Sigma Fd=50$

Mean = $A+\frac{\Sigma Fd}{\Sigma f}\times i=10+(\frac{50}{50}\times 4)=10+4=14$

Hence option (D) is correct