Question

For the Data Set below, calculate the Variance to the nearest hundredth decimal place. (Do not use a coma in your answer) 175 349 234 512 638 549 500 611

Answer 1

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

$Mean=\dfrac{\sum x}{n}$

where, n is number of observation.

$Mean=\dfrac{3568}{8}=446$

The mean of the data is 446.

$Variance=\dfrac{\sum (x-mean)^2}{n-1}$

$Variance=\dfrac{(175-446)^2+(349-446)^2+(234-446)^2+(512-446)^2+(638-446)^2+(549-446)^2+(500-446)^2+(611-446)^2}{8-1}$

$Variance=\dfrac{209764}{7}$

$Variance=29966.2857$

$Variance\approx 29966.3$

Therefore, the variance of the data is 29966.3.