Question.
The following number of goals was 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.
The following number of goals was 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.
Solution:
The number of goals scored by the team is
2, 3, 4, 5, 0, 1, 3, 3, 4, 3
Mean of data $=\frac{\text { Sum of all observations }}{\text { Total number of observations }}$
Mean score $=\frac{2+3+4+5+0+1+3+3+4+3}{10}$
$=\frac{28}{10}=2.8$
$=2.8 \mathrm{goals}$
Arranging the number of goals in ascending order,
0, 1, 2, 3, 3, 3, 3, 4, 4, 5
The number of observations is 10 , which is an even number. Therefore, median score will be the mean of $\frac{10}{2}$ i.e., $5^{\text {th }}$ and $\frac{10}{2}+1$ i.e., $6^{\text {th }}$ observation while arranged in ascending or descending order.
Median score $=\frac{5^{\text {th }} \text { observation }+6^{\text {th }} \text { observation }}{2}$ $=\frac{3+3}{2}$
$=\frac{6}{2}$
$=3$
Mode of data is the observation with the maximum frequency in data.
Therefore, the mode score of data is 3 as it has the maximum frequency as 4 in the data.
The number of goals scored by the team is
2, 3, 4, 5, 0, 1, 3, 3, 4, 3
Mean of data $=\frac{\text { Sum of all observations }}{\text { Total number of observations }}$
Mean score $=\frac{2+3+4+5+0+1+3+3+4+3}{10}$
$=\frac{28}{10}=2.8$
$=2.8 \mathrm{goals}$
Arranging the number of goals in ascending order,
0, 1, 2, 3, 3, 3, 3, 4, 4, 5
The number of observations is 10 , which is an even number. Therefore, median score will be the mean of $\frac{10}{2}$ i.e., $5^{\text {th }}$ and $\frac{10}{2}+1$ i.e., $6^{\text {th }}$ observation while arranged in ascending or descending order.
Median score $=\frac{5^{\text {th }} \text { observation }+6^{\text {th }} \text { observation }}{2}$ $=\frac{3+3}{2}$
$=\frac{6}{2}$
$=3$
Mode of data is the observation with the maximum frequency in data.
Therefore, the mode score of data is 3 as it has the maximum frequency as 4 in the data.