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.

We know that, The formula for mean, median and mode 

Mean = $\frac{sum of all obsesrvations}{Total number of observations}$

Median = Middle observation 

Here, 15 observations are given which is odd number of observation so the formula for median in case of odd number of observation iss

Median = Size of   ( $\frac{n + 1}{2}$) th observation /2

Mode = Most repeated observation

Let the given data is  41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60 

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

=  822/15

= 54.8

(ii) Median: For finding the median we first arrange the observation in ascending order as follows,

Ascending order : 39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98

Median = middle observation

=  Size of   ( $\frac{n + 1}{2}$) ^th observation /2

= size of (15 $+$ 1 /2) ^th observation  

= size of (16/2)  ^th observation  

= Size of (8) ^th 

= 52

(iii) mode = 52

because 52 repeated 3 times.