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

$\begin{gathered} x_i=each\text{ value from the data} \\ N\text{ = number of data} \\ \mu=\operatorname{mean} \end{gathered}$

Let's find the mean:

$\begin{gathered} \mu=\frac{3+4+5+6+2+3+12+79+5}{9}=\frac{119}{9}=13.2 \\ \\ \end{gathered}$

The mean is = 13.2

To find the standard deviation, we have:

$\sigma=\sqrt[]{\frac{\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[]{\frac{104.04+84.64+67.24+51.84+125.44+104.04+1.44+4239.64+67.24}{8}}$

$\begin{gathered} \sigma=\sqrt[]{\frac{4935.56}{8}} \\ \\ \sigma=\sqrt[]{616.945} \\ \\ \sigma=24.8 \end{gathered}$

Therefore, the standard deviation of the data is 24.8

ANSWER:

24.8