Question

The weight of 50 apples were recorded as given below. Calculate the mean weight to the nearest gross, by the step deviation method

weight	80-85	85-90	90-95	95-100	100-105	105-110	110-115
No. of apples	5	8	10	12	8	4	3

Answer 1

For the given data, class difference $h=85-80=5$

$CI$	$f_i$	$Classmark$ $x_i$	$d_i=\frac{x_i-A}{h}$	$f_i{d}_i$
$80-85$	$5$	$82.5$	$-3$	$-15$
$85-90$	$8$	$87.5$	$-2$	$-16$
$90-95$	$10$	$92.5$	$-1$	$-10$
$95-100$	$12$	$A=97.5$	$0$	$0$
$100-105$	$8$	$102.5$	$1$	$8$
$105-110$	$4$	$107.5$	$2$	$8$
$110-115$	$3$	$112.5$	$3$	$9$
	$\sum f_i=50$			$\sum f_i{d}_i=-16$

$\Rightarrow$ $\overline{x}=A+\frac{\sum f_i{d}_i}{\sum f_i}\times h$

$=97.5+\frac{(-16)}{50}\times 5$

$=97.5-1.6$

$=95.9$