Question

A sample was done, collecting the data below . Calculate the standard deviation , to one decimal place. 30 6 1 3 8

Answer 1

Given:

Given data is 30, 6, 1, 3, 8.

Required:

To find the standard deviation of the given data set.

Step-by-step explanation:

The formula for standard deviation is,

`\sigma=\sqrt{(1)/(N)(\sum_(i=1)^N}(xi-x)^2`

Here

`\begin{gathered} N=5 \\ x=(30+6+1+3+8)/(5) \\ \\ x=9.6 \end{gathered}`

Now

`\begin{gathered} \sigma=\sqrt{(1)/(5)}(30-9.6)^2+...(8-9.6)^2 \\ \\ =\sqrt{(1)/(5)(416.16+12.96+73.96+43.56+2.56} \\ \\ =\sqrt{(549.2)/(5)} \\ \\ =√(109.84) \\ \\ =10.48 \\ \\ \sigma=10.5 \end{gathered}`

Final Answer:

The standard deviation of the given data set is 10.5