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

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

C) $\frac { \sum ( X - \bar { X } ) } { N _ { \text {population } } }$

D) $\frac { \sum ( X - \mu ) ^ { 2 } } { N _ { \text {population } } }$

Question

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

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

C) $\frac { \sum ( X - \bar { X } ) } { N _ { \text {population } } }$

D) $\frac { \sum ( X - \mu ) ^ { 2 } } { N _ { \text {population } } }$

Quizplus · Accepted Answer

The formula for population variance is the sum of the squared differences between each data point and the population mean, divided by the total number of data points. This can be written as $\frac { \sum ( X - \mu ) ^ { 2 } } { N _ { \text {population } } }$, which is option D. Options A and C are not correct because they do not include the squaring step. Option B is the formula for sample variance, which uses a slightly different denominator (n-1) to estimate the true population variance.

Which of the Following Is the Formula for the Population ∑(X−μ)Npopulation \frac { \sum ( X - \mu ) } { N _ { \text {population } } }Npopulation ​∑(X−μ)​

Which of the Following Is the Formula for the Population $\frac { \sum ( X - \mu ) } { N _ { \text {population } } }$