Question

Obtain the mean and standard deviation for the following data set:

X	10	20	30	40	50	60	70
Y	05	15	30	35	25	27	08

Answer 1

$x$	$y$	$xy$	$x-\overline{x}$	$(x-\overline{x}{)}^2$
$10$	$05$	$50$	$-32$	$1024$
$20$	$15$	$300$	$-22$	$484$
$30$	$30$	$900$	$-12$	$144$
$40$	$35$	$1400$	$-2$	$4$
$50$	$25$	$1250$	$8$	$64$
$60$	$27$	$1620$	$18$	$324$
$70$	$08$	$560$	$28$	$784$
	$\sum y=145$	$\sum xy=6080$		$\sum (x-\overline{x}{)}^2=2828$

$\Rightarrow$ $Mean\left(\overline{x}\right)=\frac{\sum xy}{\sum y}=\frac{6080}{145}=41.93\approx 42$

$\sigma =\sqrt{\frac{\sum (x-\overline{x}{)}^2}{\sum y}}$

$=\sqrt{\frac{2828}{145}}$

$=\sqrt{19.50}$

$=4.46$