Which of the following is not an example of a mean square?
A) $\mu ^ { 2 }$
B) $\frac { n _ { 1 } ( \bar { x } 1 - \bar { x } ) + n _ { 2 } ( \bar { x } 2 - \bar { x } ) + \ldots + n _ { k } ( \bar { x } k - \bar { x } ) } { k - 1 }$
C) $\sigma ^ { 2 }$
D) $\frac { \left( \mathrm { n } _ { 1 } - 1 \right) \mathrm { s } _ { 1 } ^ { 2 } + \left( \mathrm { n } _ { 2 } - 1 \right) \mathrm { s } _ { 2 } ^ { 2 } + \ldots + \left( \mathrm { n } _ { \mathrm { k } } - 1 \right) \mathrm { s } _ { \mathrm { k } } ^ { 2 } } { \mathrm { n } - \mathrm { k } }$

Question

Which of the following is not an example of a mean square? 
A) $\mu ^ { 2 }$
B) $\frac { n _ { 1 } ( \bar { x } 1 - \bar { x } ) + n _ { 2 } ( \bar { x } 2 - \bar { x } ) + \ldots + n _ { k } ( \bar { x } k - \bar { x } ) } { k - 1 }$
C) $\sigma ^ { 2 }$
D) $\frac { \left( \mathrm { n } _ { 1 } - 1 \right) \mathrm { s } _ { 1 } ^ { 2 } + \left( \mathrm { n } _ { 2 } - 1 \right) \mathrm { s } _ { 2 } ^ { 2 } + \ldots + \left( \mathrm { n } _ { \mathrm { k } } - 1 \right) \mathrm { s } _ { \mathrm { k } } ^ { 2 } } { \mathrm { n } - \mathrm { k } }$

Quizplus · Accepted Answer

$\mu^2$ is not a mean square; it represents the square of the population mean, not a calculated mean square from sample data or variance measures. Mean squares are typically calculated from sample data or as part of variance analysis, such as in options B and D, or represent variance ($\sigma^2$) directly as in option C.

Which of the Following Is Not an Example of a Mean