2. 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.
Solution: Mean=Average = Sum of all the observations/Total number of observations = (41+39+48+52+46+62+54+40+96+52+98+40+42+52+60)/15 = 822/15 = 54.8 Median, To find the median, we first arrange the data in ascending order. 39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98 Here, Number of observations (n) = 15 Since the number of observations are odd, the median can be calculated as: Median = [(n+1)/2]th observation = [(15+1)/2]th observation = (16/2)th observation = 8th observation = 52 Mode, To find the mode, we first arrange the data in ascending order. 39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98 Here, We find that 52 occurs most frequently (3 times) ∴ Mode = 52
