Question

A golfer recorded the following scores for each of four rounds of golf: $86,81,87,82$.

The mean of the scores is $84$.

What is the sum of the squared deviations of the scores from the mean?

Answer 1

Find the sum of squared deviations about the mean:

The given data set is $86,81,87,82$.

The mean of this data set is $84$.

Then the differences in the data values from the mean are given by :

$\begin{array}{rcl}86-84& =& 2,\\ 81-84& =& -3,\\ 87-84& =& 3,\\ 82-84& =& -2\end{array}$

Then squared of these deviations about the mean are :

$\begin{array}{rcl}{\left(2\right)}^2& =& 4,\\ {(-3)}^2& =& 9,\\ {\left(3\right)}^2& =& 9,\\ {(-2)}^2& =& 4\end{array}$.

The deviation is defined as the difference between the observed value and the expected value of a variable.

So that the squared deviation from the mean is the square of the difference between data value and mean.

Then the sum of squared deviations from the mean is $4+9+9+4=26$.

Therefore, the sum of squared deviations of scores from the mean is $\mathbf{26}$.