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.

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Given:

The following number of goals were scored by a team in a series of 10 matches:

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

To do:

We have to find the mean, median and mode of these scores.

Solution:

We know that,

$\text{ Mean }=\frac{\text { Sum of all the observations }}{\text { Total number of observations}}$

Therefore,

Mean of the given scores $=\frac{2+3+4+5+0+1+3+3+4+3}{10}$

$=\frac{28}{10}$

$=2.8$

To find the median of the given data, we have to arrange the data in ascending order.

The given data in ascending order is $0, 1, 2, 3, 3, 3, 3, 4, 4, 5$

Here,

Number of observations $n = 10$ which is even

Therefore,

Median $= \frac{1}{2}[\frac{n}{2}th\ term+(\frac{n}{2}+1)th\ term]$  (when $n$ is even)

$\frac{n}{2}=\frac{10}{2}=5$

Median of the given scores $=\frac{1}{2}[5th\ term + 6th\ term]$

$=\frac{1}{2}[3+3]$

$=\frac{6}{2}$

$=3$

In the given data,

Frequency of $0$ is $1$

Frequency of $1$ is $1$

Frequency of $2$ is $1$

Frequency of $3$ is $4$

Frequency of $4$ is $2$

Frequency of $5$ is $1$

We know that,

Mode is the value or values in the data set that occur most frequently.

Therefore,

Mode of the given scores is $3$.

Updated on 10-Oct-2022 13:47:38