Question

Petroleum pollution in oceans stimulates the growth of certain bacteria. An assessment of this growth has been made by counting the bacteria in each of 6 randomly chosen specimens of ocean water (of a fixed size). The 6 counts obtained were as follows.66, 45, 65, 70, 58, 62Find the standard deviation of this sample of numbers. Round your answer to two decimal places.

Answer 1

8.81

Explanation:

The standard deviation for a sample is calculated using the formula:

`s=\sqrt{\frac{\sum^{}_{}(x-\text{Mean)}^2}{n-1}}`

First, find the mean of the data set.

`\text{Mean}=(66+45+65+70+58+62)/(6)=(366)/(6)=61`

Next, we find the square of the mean deviations for each x.

`\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}`

Therefore, the standard deviation of this sample of numbers will be:

`s=\sqrt[]{\frac{\sum^{}_{}(x-\text{Mean)}^2}{n-1}}=\sqrt[]{(388)/(6-1)}=\sqrt[]{(388)/(5)}=8.81`

The standard deviation is 8.81 (correct to 2 decimal places).