Question

The following number of goals were scored by a team in a series of $10$ matches: $2,3,4,5,0,1,3,3,4,3$.Find the mean, median, and mode of these scores.

Answer 1

Step 1: Calculate Mean:

The number of goals was scored by a team in a series of $10$ matches:

$2,3,4,5,0,1,3,3,4,3$

Mean$\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{Sum}\mathbf{}\mathbf{of}\mathbf{}\mathbf{all}\mathbf{}\mathbf{the}\mathbf{}\mathbf{elements}}{\mathbf{total}\mathbf{}\mathbf{number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{elements}}$

Mean $=\frac{(2+3+4+5+0+1+3+3+4+3)}{10}=\frac{28}{10}$

$\Rightarrow$Mean $=2.8$

Step 2: Calculate median :

Arranging the given data in ascending order, we get,

$0,1,2,3,3,3,34,4,5$

$\mathrm{n}$(number of observations)$=10$

Median $\mathbf{=}\frac{{\left(\frac{n}{2}\right)}^{\mathbf{th}}\mathbf{observations}\mathbf{+}{\displaystyle {\left(\frac{n}{2}+1\right)}^{\mathrm{th}}}\mathbf{observations}}{\mathbf{2}}$

$$\begin{gathered} =\frac{{\left({\displaystyle \frac{10}{2}}\right)}^{\mathrm{th}}\mathrm{observation}+{\left({\displaystyle \frac{10}{2}+1}\right)}^{\mathrm{th}}\mathrm{observation}}{2} \\ =\frac{5^{th}\mathrm{observation}+6^{th}\mathrm{observation}}{2} \\ =\frac{3+3}{2}=\frac{6}{2}=3 \end{gathered}$$

$\Rightarrow$Median$=3$

Step 3: Calculate Mode:

Mode of data is the observation with the maximum frequency in data.

Therefore, the mode score of data is $3$ as it has a maximum frequency of four.

$\Rightarrow$Mode$=3$

Hence, the mean$=2.8$, median$=3$, and mode$=3$ of these scores.