# NCERT Solutions for Class 7 Maths Chapter 3 Data Handling Ex 3.2

**NCERT Solutions for Class 7 Maths Chapter 3 Data Handling Exercise 3.2**

Ex 3.2 Class 7 Maths Question 1.

The scores in mathematics test (out of 25) of 15 students is as follows:

19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20

Find the mode and median of this data. Are they same?

Solution:

Given data:

19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20

Let us arrange the given data in increasing order

Since 20 occurs 4 times (highest)

∴ Mode = 20

n = 15 (odd)

∴ Median = \(\frac{n+1}{2} \text { th term }=\frac{15+1}{2}\)

= 8th term = 20

Thus, median = 20 and mode = 20

∴ Mode and median are same.

Ex 3.2 Class 7 Maths Question 2.

The runs scored in a cricket match by 11 players is as follows:

6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15

Find the mean, mode and median of this data. Are the three same?

Solution:

Given data:

6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15

Arranging the given data in increasing order, we get

Here, 15 occurs 3 times (highest)

∴ Mode = 15

n = 11 (odd)

∴ Median = \(\left(\frac{11+1}{2}\right)^{t h}\) term = 6th term = 15

Thus mean = 39, mode = 15 and median = 15

No, they are not same.

Ex 3.2 Class 7 Maths Question 3.

The weights (in kg) of 15 students of a class are:

38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47

(i) Find the mode and median of this data.

(ii) Is there more than one mode?

Solution:

Given data: 38, 42, 35, 37,45, 50, 32,43, 43,40, 36, 38, 43, 38, 47

Arranging in increasing order, we get

(i) Here, 38 and 42 occur 3 times (highest)

Thus mode = 38 and 43

n = 15(odd)

Median = \(\left(\frac{n+1}{2}\right)^{\mathrm{th}} \text { term }=\left(\frac{15+1}{2}\right)^{\mathrm{th}}\) term

= 8th term = 40

Thus mode 38 and 43 and median = 40

(ii) Yes, the given data has two modes i.e. 38 and 43.

Ex 3.2 Class 7 Maths Question 4.

Find the mode and median of the data:

13, 16, 12, 14, 19, 12, 14, 13, 14

Solution:

Arranging the given data in increasing order, we get

Here, 14 occur 3 times (highest)

Thus, mode = 14

n = 9(odd)

∴ Median = \(\left(\frac{n+1}{2}\right)^{\text { th }} \text { term }=\left(\frac{9+1}{2}\right)^{\text { th }}\) term

= 5th term = 14

Hence, mode = 14 and median = 14.

Ex 3.2 Class 7 Maths Question 5.

Tell whether the statement is true or false.

(i) The mode is always one of the number in a data.

(ii) The mean is one of the numbers in a data.

(iii) The median is always one of the numbers in a data.

(iv) The data 6, 4, 3, 8, 9, 12, 13, 9 has mean 9.

Solution:

(i) True

(ii) False

(iii) True

(iv) False