Which of the following is the formula for the variance of a sample used to estimate the 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 variance of a sample used to estimate the 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 the variance of a sample used to estimate the population variance is given by Option D, which is $\frac { \sum ( X - \bar { X } ) ^ { 2 } } { N - 1 }$. This is because the denominator in the formula is N - 1, as the sample variance is estimated using the sample mean instead of the population mean. Option A is incorrect because it does not include the squared deviations, and Option B is incorrect because it uses N instead of N-1 as the denominator. Option C is the formula for the sample variance, not the variance of the sample used to estimate the population variance.

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

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