# What are the mean and standard deviation of {34, 98, 20, -1200, -90}?

Apr 11, 2018

Mean = 227.6
Standard deviation = 489.9492

#### Explanation:

Calculate the mean as the sum of the numbers divided by the number of observations

Mean $= \frac{34 + 98 + 20 - 1200 - 90}{5} = 227.6$

Calculate the standard deviation as the square root of the sum of the squared difference each observation and the mean divided by the number of observations.

Standard deviation $= \sqrt{\frac{{\left(34 - 227.6\right)}^{2} + {\left(98 - 227.6\right)}^{2} + {\left(20 - 227.6\right)}^{2} + {\left(- 1200 - 227.6\right)}^{2} + {\left(- 90 - 227.6\right)}^{2}}{5}} = 489.9492$

Apr 11, 2018

Mean: $- 227.6$, standard deviation is $489.9492$

#### Explanation:

Data: $S = \left\{34 , 98 , 20 , - 1200 , - 90\right\}$

Mean : $\sum \frac{s}{5} = - 227.6$

Variance square differences are ${\left(34 - \left(- 227.6\right)\right)}^{2} = 68434.56$,

${\left(98 - \left(- 227.6\right)\right)}^{2} = 106015.36$, ${\left(20 - \left(- 227.6\right)\right)}^{2} = 61305.76$,

${\left(- 1200 - \left(- 227.6\right)\right)}^{2} = 945561.76$, ${\left(- 90 - \left(- 227.6\right)\right)}^{2} = 18933.76$

Average variance square differences is

${\sigma}^{2} = \frac{1200251.2}{5} = 240050.24$

Standard deviation is $\sqrt{{\sigma}^{2}} = 489.9492$