Find the arithmetic mean (correct to the nearest whole-number) by… - Vidyadip

Question

Find the arithmetic mean $($correct to the nearest whole$-$number$)$ by using step$-$deviation method.

$x$	$5$	$10$	$15$	$20$	$25$	$30$	$35 $	$40$	$45$	$50$
$f$	$20$	$43$	$75$	$67$	$72$	$45$	$39$	$9$	$8$	$6$

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Answer

Let the assumed mean $A = 30$

$x$	$f$	$d=x-A$	$t=(x-A)/(i)=(x-30)/(5)$	$ft$
$5$	$20 $	$-20$	$-5$	$-100$
$10$	$43$	$-15$	$-3$	$-129$
$15$	$75$	$-10$	$-2$	$-150$
$20$	$67$	$-5$	$-1$	$-67$
$A=25$	$72$	$0$	$0$	$0$
$30$	$45$	$5$	$1$	$45$
$35$	$39$	$10$	$2$	$78$
$40$	$9$	$15$	$3$	$27$
$45$	$8$	$20$	$4$	$32$
$50$	$6$	$25$	$5$	$30$
	Sigma $f=384$			Sigma $ft=-234$

$\therefore \text { Mean }= A +\frac{\Sigma f t}{\Sigma f} \times i$
$=30+\frac{(-598)}{384} \times 5$
$=30-\frac{299}{192} \times 5$
$=30-\frac{1495}{192}$
$=\frac{5760-1495}{192}$
$=\frac{14265}{192}$
$=22.21$
$=22$

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