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

What are the mean and standard deviation of {34, 98, 20, -1200, -90}?
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Jaxson White
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
$=\sqrt{\frac{\left(34-227.6{\right)}^{2}+\left(98-227.6{\right)}^{2}+\left(20-227.6{\right)}^{2}+\left(-1200-227.6{\right)}^{2}+\left(-90-227.6{\right)}^{2}}{5}}=489.9492$
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balafiavatv
Data: S={34,98,20,-1200,-90}
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 $\sqrt{{\sigma }^{2}}=489.9492$
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