Question

The following table shows the heights $\left(cm\right)$ of $50$ girls of class $X$ of a school.

Height $\left(cm\right)$	Number of girls
$120-130$	$2$
$130-140$	$8$
$140-150$	$12$
$150-160$	$20$
$160-170$	$8$
$Total$	$50$

Find the mean of the above data by step deviation method.

Answer 1

$\Rightarrow$ $A=145$ and $h=10$

$Class-Interval$	$Class-mark$ $x_i$	$Frequency$ $f_i$	$u_i=\frac{x_i-A}{h}$	$f_i{u}_i$
$120-130$	$125$	$2$	$-2$	$-4$
$130-140$	$135$	$8$	$-1$	$-8$
$140-150$	$145=A$	$12$	$0$	$0$
$150-160$	$155$	$20$	$1$	$20$
$160-170$	$165$	$8$	$2$	$16$
		$\sum f_i=50$		$\sum f_i{u}_i=24$

$Mean=A+\frac{\sum f_i{u}_i}{\sum f_i}\times h$

$=145+\frac{24}{50}\times 10$

$=145+4.8$

$=149.8$