Question

*Calculate the standard deviation of the following data. 3,4,5,6,2,3,12,79,5

Answer 1

Given the data:

3, 4, 5, 6, 2, 3, 12, 79, 5​

To find the standard deviation, use the formula:

`\sigma=\sqrt[]{\frac{\sum ^{}_{}(x_i-\mu)^2}{N-1}}`

Where

Let's find the mean:

`\begin{gathered} \mu=(3+4+5+6+2+3+12+79+5)/(9)=(119)/(9)=13.2 \\ \\ \end{gathered}`

The mean is = 13.2

To find the standard deviation, we have:

`\sigma=\sqrt[]{(\mleft(3-13.2\mright)^2+(4-13.2)^2+(5-13.2)^2+(6-13.2)^2+(2-13.2)^2+(3-13.2)^2+(12-13.2)^2+(79-13.2)^2+(5-13.2)^2)/(9-1)}`
`\sigma=\sqrt[]{(104.04+84.64+67.24+51.84+125.44+104.04+1.44+4239.64+67.24)/(8)}`

`\begin{gathered} \sigma=\sqrt[]{(4935.56)/(8)} \\ \\ \sigma=\sqrt[]{616.945} \\ \\ \sigma=24.8 \end{gathered}`

Therefore, the standard deviation of the data is 24.8

ANSWER:

24.8