Question

The following tables shows the weights of 12 students:

Weight (in kg):	67	70	72	73	75
Number of students:	4	3	2	2	1

Find the mean weight by using short-cut method.

Answer 1

Let the assumed mean be A= 72
Calculation of Mean

$x_i$	$f_i$	$d_i=x_i-A=x_i-72$	$f_i{d}_i$
$67$	$4$	$-5$	$-20$
$70$	$3$	$-2$	$-6$
$72$	$2$	$0$	$2$
$73$	$2$	$1$	$2$
$75$	$2$	$3$	$3$
	$N=\sum f_i=12$		$\sum f_i{d}_i=-21$

We have,

$N=12,\sum f_i{d}_i=-21$, and A = 72

$\therefore Mean=A+\frac{1}{N}(\sum f_i{d}_i)$

$\therefore Mean=72+\frac{-21}{12}=72-\frac{7}{4}$

$\therefore Mean=\frac{288-7}{4}=\frac{281}{4}=70.25kg$

Hence, mean weight = $70.25$ kg.