# 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.

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