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:

The mean (or average) of a number of observations is the sum of the values of all the observations divided by the total number of observations.

The median is the value of the given number of observations, which divides it into exactly two parts. So, when the data is arranged in ascending (or descending) order the median of ungrouped data can be calculated based on the number of observations being even or odd.

The mode is that value of the observation which occurs most frequently.

The marks of 15 students in mathematics test are:

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

Mean of data = Sum of all 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

Arranging the scores obtained by 15 students in 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 (15 + 1)/2 = 8^th observation

Therefore, the median of the data = 52

The mode of data is the observation with the maximum frequency in data.

Therefore, the mode of this data is 52 having the highest frequency of 3.

☛ Check: NCERT Solutions for Class 9 Maths Chapter 14

Video Solution:

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.

NCERT Solutions for Class 9 Maths Chapter 14 Exercise 14.4 Question 2

Summary:

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. The mean, median, and mode of this data are 54.8, 52, and 52 respectively.

☛ Related Questions:

• The following number of goals were scored by a team in a series of 10 matches:2, 3, 4, 5, 0, 1, 3, 3, 4, 3Find the mean, median and mode of these scores.
• The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.29, 32, 48, 50, x, x + 2, 72, 78, 84, 95
• Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.
• Find the mean salary of 60 workers of a factory from the following table: