The variance of $\bar { Y } , \sigma \frac { 2 } { Y }$ , is given by the following formula:
A) $\sigma \frac { 2 } { Y }$
B) $\frac { \sigma _ { y } } { \sqrt { n } }$
C) $\frac { \sigma _ { \gamma } ^ { 2 } } { n }$
D) $\frac { \sigma _ { y } ^ { 2 } } { \sqrt { n } }$

Question

Quizplus · Accepted Answer

The variance of the sample mean $\bar{Y}$ is given by $\frac{\sigma_{y}^{2}}{n}$, where $\sigma_{y}^{2}$ is the population variance and $n$ is the sample size. This formula reduces the variance of the mean as the sample size increases, reflecting the increased accuracy of $\bar{Y}$ as an estimator of the population mean with larger samples.

The Variance Of Yˉ,σ2Y\bar { Y } , \sigma \frac { 2 } { Y }Yˉ,σY2​

The Variance Of $\bar { Y } , \sigma \frac { 2 } { Y }$