Question

The marks obtained by $40$ students of Class XII of a certain school in a Science paper consisting of $200$ marks are presented in table below. Find the mean of the marks obtained by the students using step deviation method.

• A. $153.5$
• B. $154.5$
• C. $150.2$
• D. $156.5$

Answer 1

Answer: (A)

$153.5$

Answer:- Using Shortcut Method

Class interval width (i) = $120-100=20$

Marks	X	Students (F)	$d=\frac{X-A}{i}$	Fd
100-120	110	4	-2	-8
120-140	130	5	-1	-5
140-160	150 = A	11	0	0
160-180	170	20	1	20
		$\Sigma F=40$		$\Sigma Fd=7$

Mean ( By step deviation formula) = $A+\frac{\Sigma Fd}{\Sigma F}\times i=150+(\frac{7}{40}\times 20)=150+3.5+=153.5$

A) Mean = $153.5$