Answer:
8.81
Explanation:
The standard deviation for a sample is calculated using the formula:
[tex]s=\sqrt{\frac{\sum^{}_{}(x-\text{Mean)}^2}{n-1}}[/tex]
First, find the mean of the data set.
[tex]\text{Mean}=\frac{66+45+65+70+58+62}{6}=\frac{366}{6}=61[/tex]
Next, we find the square of the mean deviations for each x.
[tex]\begin{gathered} \sum (x-\text{Mean)}^2=(66-61)^2+(45-61)^2+\mleft(65-61\mright)^2 \\ +\mleft(70-61\mright)^2+(58-61)^2+(62-61)^2 \\ =(5)^2+(-16)^2+(4)^2+(9)^2+(-3)^2+(1)^2 \\ =25+256+16+81+9+1 \\ \sum (x-\text{Mean)}^2=388 \end{gathered}[/tex]
Therefore, the standard deviation of this sample of numbers will be:
[tex]s=\sqrt[]{\frac{\sum^{}_{}(x-\text{Mean)}^2}{n-1}}=\sqrt[]{\frac{388}{6-1}}=\sqrt[]{\frac{388}{5}}=8.81[/tex]
The standard deviation is 8.81 (correct to 2 decimal places).
