Which of the following gives the variance of observations in terms of the arithmetic…

MATHEMATICS · Single correct · A Level · Mathematics · Data presentation and interpretation · Data presentation and interpretation

Problem

Which of the following gives the variance

\sigma^{2}

n

observations

x_{1},x_{2},\dots ,x_{n}

in terms of the arithmetic mean

\bar{x}

and the sum of squares

\sum x_{i}^{2}

? (a)

\displaystyle \sigma^{2}=\dfrac{\sum x_{i}^{2}}{n}+\bar{x}^{2}

(b)

\displaystyle \sigma^{2}=\dfrac{\sum x_{i}^{2}-n\bar{x}^{2}}{n-1}

(c)

\displaystyle \sigma^{2}=\dfrac{\sum x_{i}^{2}}{n}-\bar{x}^{2}

(d)

\displaystyle \sigma^{2}=\dfrac{\sum x_{i}^{2}}{\,n-1}-\bar{x}^{2}