Question

Find the mean of the following frequency distribution by the short cut method.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	$9$	$12$	$15$	$10$	$14$

Answer 1

Class Interval	Mean Value $\left(x\right)$	Frequency $\left(f\right)$	$d=x-A$	$f\times d$
$0-10$	$5$	$9$	$-20$	$-180$
$10-20$	$15$	$12$	$-10$	$-120$
$20-30$	$A=25$	$15$	$0$	$0$
$30-40$	$35$	$10$	$10$	$100$
$40-50$	$45$	$14$	$20$	$280$
		$\Sigma f=60$		$\Sigma fd=80$

From the table $A=25$

Mean, $\overline{x}=A+\frac{\Sigma fd}{\Sigma f}$

$\Rightarrow \overline{x}=25+\frac{80}{60}$

$\Rightarrow \overline{x}=25+1.33$

$\Rightarrow \overline{x}=26.33$

Hence, the mean is $26.33$.