How do you find the mean and standard deviation of the data set 82, 44, 67, 52, 120?

Jun 23, 2017

Mean is $73.0$ , standard deviation is $26.86$

Explanation:

Data set : $\left\{82 , 44 , 67 , 52 , 120\right\}$

Mean is the average of Data set, $M = 82 + 44 + 67 + 52 + 120 = \frac{365}{5} = 73.0$

Standard deviation is square root of variance$\left({\sigma}^{2}\right)$ , $S D = \sqrt{{\sigma}^{2}}$

Variance is The average of the squared differences from the Mean.

${\sigma}^{2} = \frac{{\left(82 - 73\right)}^{2} + {\left(44 - 73\right)}^{2} + {\left(67 - 73\right)}^{2} + {\left(52 - 73\right)}^{2} + {\left(120 - 73\right)}^{2}}{5}$ or
${\sigma}^{2} = \frac{81 + 841 + 36 + 441 + 2209}{5} = \frac{3608}{5} = 721.6 \therefore$

$S D = \sqrt{{\sigma}^{2}} = \sqrt{721.6} \approx 26.86$

Mean is $73.0$ , standard deviation is $26.86$ [Ans]