Answer:
The variance of the data is 29966.3.
Step-by-step explanation:
The given data set is
175, 349, 234, 512, 638, 549, 500, 611
We need to find the variance to the nearest hundredth decimal place.
Mean of the data
[tex]Mean=\dfrac{\sum x}{n}[/tex]
where, n is number of observation.
[tex]Mean=\dfrac{3568}{8}=446[/tex]
The mean of the data is 446.
[tex]Variance=\dfrac{\sum (x-mean)^2}{n-1}[/tex]
[tex]Variance=\dfrac{(175-446)^2+(349-446)^2+(234-446)^2+(512-446)^2+(638-446)^2+(549-446)^2+(500-446)^2+(611-446)^2}{8-1}[/tex]
[tex]Variance=\dfrac{209764}{7}[/tex]
[tex]Variance=29966.2857[/tex]
[tex]Variance\approx 29966.3[/tex]
Therefore, the variance of the data is 29966.3.
