Which of the following is the formula for the estimated population variance?
A) $\frac { \sum ( X - \bar { X } ) } { N }$

B) $\frac { \sum ( X - \bar { X } ) ^ { 2 } } { N }$

C) $\frac { \sum ( X - \bar { X } ) } { N - 1 }$

D) $\frac { \sum ( X - \bar { X } ) ^ { 2 } } { N - 1 }$

Question

Which of the following is the formula for the estimated population variance? 
A) $\frac { \sum ( X - \bar { X } ) } { N }$

B) $\frac { \sum ( X - \bar { X } ) ^ { 2 } } { N }$

C) $\frac { \sum ( X - \bar { X } ) } { N - 1 }$

D) $\frac { \sum ( X - \bar { X } ) ^ { 2 } } { N - 1 }$

Quizplus · Accepted Answer

The formula for estimated population variance is the sum of the squared differences between each observation and the sample mean, divided by the degrees of freedom (N-1). This is represented by formula D, $\frac{\sum(X-\bar{X})^{2}}{N-1}$. Option A and C only consider the sum of the differences and do not square them, which leads to an incorrect estimate of variance. Option B takes the sum of squared differences but divides it by N rather than N-1, which leads to an underestimate of the population variance.

Which of the Following Is the Formula for the Estimated ∑(X−Xˉ)N\frac { \sum ( X - \bar { X } ) } { N }N∑(X−Xˉ)​

Which of the Following Is the Formula for the Estimated $\frac { \sum ( X - \bar { X } ) } { N }$