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

Sagot :

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.

Explanation:

Now variation is

[tex]s^2=\frac{\sum_{i\mathop{=}1}^n(x_i-x)^2}{n-1}[/tex]

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

Therefore,

[tex]\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}[/tex]

[tex]\begin{gathered} s^2=\frac{112.25}{12-1} \\ \\ =\frac{112.25}{11} \\ \\ =10.2045 \end{gathered}[/tex]

Final Answer:

[tex]10.2045[/tex]

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