Question

The number of goals scored by a hockey team in $20$ matches is given here:
$4,6,3,2,2,4,1,5,3,0,4,5,4,5,4,0,4,3,6,4$.
Find the mean.

Answer 1

To find the mean, let us prepare a frequency distribution table first. We observe that some scores are repeated. So to find the sum of all scores, we have to multiply each score with its frequency and then find the sum.

Scores$\left(x_i\right)$	Frequency$\left(f_i\right)$	$f_i{x}_i$
$0$	$2$	$0$
$1$	$1$	$1$
$2$	$2$	$4$
$3$	$3$	$9$
$4$	$7$	$28$
$5$	$3$	$15$
$6$	$2$	$12$
	$\sum N=20$	$\sum f_i{x}_i=69$

To do this, let us denote the scores by $x_i$ and frequency by $f_i$, then multiply $f_i$ and $x_i$ and add the product $f_i{x}_i$. Here $\sum f_i{x}_i$ denotes the sum of all the product $f_i\times x_i$. Now the mean is

$\begin{array}{cc}\overline{X}& =\frac{\text{sum of the scores}}{\text{number of scores}}\\ & =\frac{\sum f_i{x}_i}{N}\\ & =\frac{69}{20}\end{array}$
Thus, we get mean goals scored $\overline{X}=\mathrm{3.45.}$