Question

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

Answer 1

Mean = 227.6
Standard deviation = 489.9492

Explanation:

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

Mean `=(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( ( (34 - 227.6)^2 + (98 - 227.6)^2 + (20 - 227.6)^2 + ( - 1200 - 227.6)^2 +( - 90 - 227.6)^2 ) / 5 ) = 489.9492`

Answer 2

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

Explanation:

Data: `S= {34,98,20,-1200,-90}`

Mean : `sum s/5= -227.6`

Variance square differences are `(34-(-227.6))^2=68434.56`,

`(98-(-227.6))^2=106015.36`, `(20-(-227.6))^2=61305.76`,

`(-1200-(-227.6))^2=945561.76`, `(-90-(-227.6))^2=18933.76`

Average variance square differences is

`sigma^2=1200251.2/5=240050.24`

Standard deviation is `sqrt(sigma^2)=489.9492`