Question

Whats the variance and the standard deviation of the data set 6,9,2,5,4,10,3,12,2,7,7,8

Answer 1

Given:

6,9,2,5,4,10,3,12,2,7,7,8

Required:

To find the variation and standard deviation of the given data set.

Step-by-step explanation:

Now variation is

`s^2=\frac{\sum_{i\mathop{=}1}^n(x_i-x)^2}{n-1}`

The numerator in the above is sum of the square of the given data.

Therefore,

`\begin{gathered} =(6-6.25)^2+(9-6.25)^2+(2-6.25)^2+(5-6.25)^2+(4-6.25)^2+(10-6.25)^2+ \\ (3-6.25)^2+(12-6.25)^2+(2-6.25)^2+(7-6.25)^2+(7-6.25)^2+(8-6.25)^2 \end{gathered}`

`\begin{gathered} s^2=(112.25)/(12-1) \\ \\ =(112.25)/(11) \\ \\ =10.2045 \end{gathered}`

Final Answer:

`10.2045`