Question

The frequency distribution of marks in English are given in the table:

Marks	50-60	60-70	70-80	80-90
Number of students	12	24	14	10

Find the mean by step deviation method.

• A. $58$
• B. $48$
• C. $69$
• D. $71$

Answer 1

The correct option is C $69$

$X$	Mid point(x)	Frequency (F)	i=class interval width	A=65 Assumed mean	u=$\frac{x-A}{i}$	fu
$50-60$	$55$	$12$	$10$	$65$	$-1$	$-12$
$60-70$	$65=A$	$24$	$10$	$65$	$0$	$0$
$70-80$	$75$	$14$	$10$	$65$	$1$	$14$
$80-90$	$85$	$10$	$10$	$65$	$2$	$20$
		$\Sigma f=60$				$\Sigma fu=22$

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
$\sum f=$ 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
$\overline{X}=65+\frac{22}{60}\times 10$
$=65+3.666$
$=68.666$ $\approx$ $69$ marks