Question

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.

Answer 1

The marks of 15 students in mathematics test are
41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60
$\text{Mean of data}=\frac{\text{Sum of all observations}}{\text{Total number of observations}}$
$=\frac{41+39+48+52+46+62+54+40+96+52+98+40+42+52+60}{15}$
$=\frac{822}{15}=54.8$

Arranging the scores obtained by 15 students in an ascending order,
39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98
As the number of observations is 15 which is odd, therefore, the median of data will be $\frac{15+1}{2}$ = 8th observation whether the data is arranged in an ascending or descending order.
Therefore, median score of data = 52

Mode of data is the observation with the maximum frequency in data. Therefore, mode of this data is 52 having the highest frequency in data as 3.