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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