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}=\frac{\sum ^{\infty}_{i\mathop=0}xi}{n}$$\begin{gathered} \bar{x}=\frac{40+50+55+57+57+57+60}{7} \\ \bar{x}=\frac{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

$\begin{gathered} \sigma=\sqrt[]{\frac{275.4}{7}} \\ \sigma=6.272\approx6.3 \end{gathered}$