Question

Find the population standard deviation for the following data points. 40 50 55 57 57 57 60What is x bar: _____What is the sum of the square deviations: _____What is tha sample standard deviation: _____Round all to the nearest tenth.

Answer 1

start by calculating the mean of the data using the formula

`\bar{x}=(\sum ^(\infty)_(i\mathop=0)xi)/(n)`
`\begin{gathered} \bar{x}=(40+50+55+57+57+57+60)/(7) \\ \bar{x}=(376)/(7) \\ \bar{x}=53.714\approx53.7 \end{gathered}`

now use the formula for the standard deviation

`\sigma=\sqrt[]{\sum^(\infty)_(i\mathop=0)}\frac{(x_i-\bar{x})^2}{n}`

find the sum of the standard deviations

`(40-53.7)^2+(50-53.7)^2+(55-53.7)^2+(57-53.7)^2+(57-53.7)^2+(57-53.7)^2+(60-53.7)^2`
`\begin{gathered} =187.69+13.69+1.69+10.89+10.89+10.89+30.69 \\ =275.43\approx275.4 \end{gathered}`

now find the standard deviation

`\begin{gathered} \sigma=\sqrt[]{(275.4)/(7)} \\ \sigma=6.272\approx6.3 \end{gathered}`