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# In a mathematics test given to 15 students, the following marks (out of 100 ) are recorded:

$41,39,48,52,46,62,54,40,96,52,98,40,42,52,60$

Find the mean, median and mode of this data.

Given:

In a mathematics test given to 15 students, the following marks (out of 100 ) are recorded:

$41,39,48,52,46,62,54,40,96,52,98,40,42,52,60$

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 data $=\frac{41+39+48+52+46+62+54+40+96+52+98+40+42+52+60}{15}$

$=\frac{822}{15}$

$=54.8$

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

The given data in ascending order is $39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98$

Here,

Number of observations $n = 15$ which is odd.

Therefore,

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

$n+1=15+1=16$

Median of the given data $=\frac{1}{2}[16th\ term]$

$=8th\ term$

$=52$

In the given data,

Frequency of $39$ is $1$

Frequency of $40$ is $2$

Frequency of $41$ is $1$

Frequency of $42$ is $1$

Frequency of $46$ is $1$

Frequency of $48$ is $1$

Frequency of $52$ is $3$

Frequency of $54$ is $1$

Frequency of $60$ is $1$

Frequency of $62$ is $1$

Frequency of $96$ is $1$

Frequency of $98$ is $1$

We know that,

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

Therefore,

Mode of the given data is $52$.

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