Mathematics

Problem

For a set of

n

observations with mean

\bar{x}

, which one of the following expressions is exactly equal to

\sum_{i=1}^{n}(x_i-\bar{x})^{2}

? a)

\sum x_i^{2}+n\,\bar{x}^{2}

\sum x_i^{2}-n\,\bar{x}^{2}

\dfrac{\sum x_i^{2}}{n}-\bar{x}^{2}

(\sum x_i)^{2}-n\,\bar{x}^{2}