Chapter 1.3, Problem 3.2CYU

To determine

To draw: A table that shows each value its deviation from mean and its squared deviation from the mean.

Answer to Problem 3.2CYU

Thus Deviation from the calculated mean is $5.59$ . And squared of deviation of mean is $31.24$ .

Explanation of Solution

Given information:

  $67,72,76,84$

For the given data $67,72,76,84$ table is,

$x$	$\left(x-\overline{x}\right)$	${\left(x-\overline{x}\right)}^2$
$67$	$-8$	$64$
$72$	$-3$	$9$
$76$	$1$	$1$
$76$	$1$	$1$
$84$	$9$	$81$
Total   $=375$	$0$	$156$

Mean is calculated as,

  $\begin{array}{l}\overline{x}=\frac{{\displaystyle \sum x_i}}{N}\\ \overline{x}=\frac{375}{5}\\ \overline{x}=75\end{array}$

Thus, mean is $75$ .

Deviation from the calculated mean is

  $\begin{array}{l}\sigma =\sqrt{\frac{{\displaystyle \sum {\left(x_i-\mu \right)}^2}}{N}}\\ =\sqrt{\frac{{\left(67-75\right)}^2+{\left(72-75\right)}^2+{\left(76-75\right)}^2+{\left(76-75\right)}^2+{\left(84-75\right)}^2}{5}}\\ =\sqrt{31.20}\\ =5.59\end{array}$

Thus, deviation from the calculated mean is $5.59$ . And squared of deviation of mean is $31.24$ .