Question

Marks	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70- 80	80-90	90-100
Frequency	3	5	6	7	8	9	10	12	6	4

Find the mean mark using step deviation method:

• A. $54$
• B. $55$
• C. $56$
• D. $57$

Answer 1

The correct option is A $54$

X	Mid Point (X)	Frequency (F)	i=class interval width	A=45 Assumed mean	u=$\frac{x-A}{i}$	fu
0-10	5	3	10	45	-4	-12
10-20	15	5	10	45	-3	-15
20-30	25	6	10	45	-2	-12
30-40	35	7	10	45	-1	-7
40-50	45=A	8	10	45	0	0
50-60	55	9	10	45	1	9
60-70	65	10	10	45	2	20
70-80	75	12	10	45	3	36
80-90	85	6	10	45	4	24
90-100	95	4	10	45	5	20
		$\Sigma f=70$				$\Sigma fu=63$

The formula used for arithmetic mean of grouped data by step deviation method is, $\overline{X}=A+\frac{\sum fu}{\sum f}\times i$
$A=$ Assumed mean of the given data
$\sum$ = Summation of the frequencies given in the grouped data
$\sum fu$ = Summation of the frequencies and deviation of a given mean data
$u=\frac{(x-A)}{i}$
$i=$ Class interval width
$\overline{X}$ = arithmetic mean
$\overline{X}=45+\frac{63}{70}\times 10$
$=45+9$
$=54$