Answer to Question #323840 in Statistics and Probability for ella

Question

Find the variance of the sampling distribution of means 2,5,7,8.

Answer 1

$2,5,7,8\\For\,\,the\,\,population\\\mu =\frac{2+5+7+8}{4}=5.5\\\sigma ^2=\frac{\left( 2-5.5 \right) ^2+\left( 5-5.5 \right) ^2+\left( 7-5.5 \right) ^2+\left( 8-5.5 \right) ^2}{4}=5.25\\For\,\,the\,\,sample\,\,of\,\,size\,\,n\in \left\{ 1,2,3,4 \right\} :\\{\sigma ^2}_{\bar{x}}=\frac{\sigma ^2}{n}=\frac{5.25}{n}$