Mathematics

Problem

Which of the following expressions equals the population variance

\sigma^{2}

for a grouped frequency distribution with

N=\sum f_i

observations? a)

\displaystyle \sigma^{2}=\frac{\left(\sum f_i x_i\right)^{2}}{\sum f_i}-\bar{x}^{2}

\displaystyle \sigma^{2}=\frac{\sum f_i\,(x_i-\bar{x})^{2}}{\sum f_i}

\displaystyle \sigma^{2}=\frac{\sum f_i\,(x_i-\bar{x})^{2}}{\sum f_i-1}

\displaystyle \sigma^{2}=\frac{\sum f_i x_i^{2}}{\sum f_i}-\bar{x}