Chapter 1.3, Problem 3.3CYU

To determine

To Find: Variance and standard deviation from the table.

Answer to Problem 3.3CYU

Thus, Sample variance is $39$ and standard deviation is $6.2449$ .

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 $75$ .

Sample variance is calculated as,

  $\begin{array}{l}=\frac{{\displaystyle \sum {\left(xi-\overline{x}\right)}^2}}{n-1}\\ =\frac{156}{4}\\ =39\end{array}$

Standard deviation is calculated as,

  $\begin{array}{l}\sigma =\sqrt{sample\mathrm{var}iance}\\ \sigma =\sqrt{39}\\ =6.2449\end{array}$

Standard deviation is the measure of dispersion of a set of data from its mean. It is measure the absolute variability of distance. Higher the dispersion the greater is the standard deviation.

Thus, Sample variance is $39$ and standard deviation is $6.2449$ .