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The marks in a subject for 12 students are as follows:
31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29
For the given data, find the (a) Range (b) Mean (c) Median (d) Mode

Solution:

Given, the data is 31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29

We have to find the range, mean, median and mode of the given data.

Arranging the data in ascending order, we get

17, 18, 23, 25, 29, 31, 35, 35, 35, 37, 38, 42

(a) We know that the difference between the highest and lowest observations in a given data is called its Range.

Highest observation = 42

Lowest observation = 17

Range = highest observation - lowest observation

= 42 -17

= 25

Therefore, the range is 25

(b) We know, mean = sum of all observations / number of observations

Sum of all observations = 17 + 18 + 23 + 25 + 29 + 31 + 35 + 35 + 35 + 37 + 38 + 4

= 365

Number of observations = 12

Mean = 365/12

= 30.41

Therefore, the mean is 30.41

(c) When the given data is arranged in ascending (or descending) order, then the middle most observation is the median of the data.

If n is even, then median = [(n/2)th term + (n/2 + 1)th term]/2

Median = [(12/2)th term + (12/2 + 1)th term]/2

= [6th term + (6+1)th term]/2

= [6th term + 7th term]/2

= (31+35)/2

= 66/2

= 33

Therefore, the median is 33.

(d) A mode is defined as the value that has a higher frequency in a given set of data.

17, 18, 23, 25, 29, 31, 37, 38, 42 occurs one time

35 occurs 3 times

Mode = 35

Therefore, the mode is 35.

✦ Try This: The marks in a subject for 12 students are as follows: 33, 35, 45, 28, 32, 43, 27, 28, 55, 15, 25, 39. For the given data, find the (a) Range (b) Mean

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 3

NCERT Exemplar Class 7 Maths Chapter 3 Problem 54

The marks in a subject for 12 students are as follows: 31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29, For the given data, find the (a) Range (b) Mean (c) Median (d) Mode

Summary:

The marks in a subject for 12 students are as follows: 31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29, The range, mean, median and mode of the given data is 25, 30.41, 33 and 35.

☛ Related Questions:

The marks in a subject for 12 students are as follows: 31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29 For the given data, find the (a) Range (b) Mean (c) Median (d) Mode

The marks in a subject for 12 students are as follows: 31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29, For the given data, find the (a) Range (b) Mean (c) Median (d) Mode

The marks in a subject for 12 students are as follows:
31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29
For the given data, find the (a) Range (b) Mean (c) Median (d) Mode