Question

Using step deviation method find the mean.

X	20-40	40-60	60-80	80-100
frequency	4	8	12	16

• A. $40$
• B. $50$
• C. $60$
• D. $70$

Answer 1

Answer: (D)

$70$

X	Mid point (X)	Frequency (F)	i=class interval width	A=50 Assumed Means	u=$\frac{x-A}{i}$	fu
20-40	30	4	20	50	-1	-4
40-60	50=A	8	20	50	0	0
60-80	70	12	20	50	1	12
80-100	90	16	20	50	2	32
		$\Sigma f=40$				$\Sigma fu=40$

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
$\overline{X}=50+\frac{40}{40}\times 20$
$=50+20$
$=70$