A set of 10 scores has a sum of squares value of 490. What is the variance?
A) 4900
B) 49
C) 7
D) 70

Question

Quizplus · Accepted Answer

To find the variance, we need to divide the sum of squares by the sample size and then subtract the mean squared. However, we do not have enough information to find the mean, so we cannot use this formula directly.

Instead, we can use the formula: 
variance = (sum of squares - (sum)^2/n) / (n-1)

Plugging in the given values, we get: 
variance = (490 - (sum)^2/10) / 9

Since we do not know the value of the sum, we cannot simplify this expression any further. Therefore, the answer must be one of the available choices.

Checking each choice: 
A) 4900 - This is simply the sum of squares multiplied by 10. It is not the correct formula for variance.

B) 49 - We calculated the numerator of the variance formula above to be 490 - (sum)^2/10. Since this is divided by 9, the denominator must be 10-1=9. Therefore, the variance simplifies to 49.

C) 7 - This is not a possible answer, as the variance cannot be smaller than the smallest score.

D) 70 - This is simply the sum of squares divided by 10. It is not the correct formula for variance.

Therefore, the only correct choice is B.

A Set of 10 Scores Has a Sum of Squares