NCERT Solutions Class 7 Maths Chapter 3 Data Handling Ex 3.2

NCERT Solutions Class 7 Mathematics 
Chapter – 3 (Data Handling)

The NCERT Solutions in English Language for Class 7 Mathematics Chapter – 3 Data Handling Exercise 3.2 has been provided here to help the students in solving the questions from this exercise. 

Chapter : 3 Data Handling

• NCERT Solution Class 7 Maths Exercise – 3.1
• NCERT Solution Class 7 Maths Exercise – 3.3
• NCERT Solution Class 7 Maths Exercise – 3.4

Exercise – 3.2 

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 –
Let us arrange the given data in increasing order
5, 9, 10, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25, 25
Since 20 occurs 4 times (highest)
∴ Mode = 20
n = 15 (odd)
∴ Median = th term = = 8^thterm
Then, value of 8^th term = 20
Hence, the median is 20.
Yes, both Mode and median values are same.

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 –
Arranging the given data in increasing order, we get
6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120
Mean of the given data = (Sum of all observations)/ (Total number of observations)
= = = 39

Here, 15 occurs 3 times (Highest)
∴ Mode = 15
n = 11 (odd)
∴ Median = th term 
Median = th term = 6^th term.
Then, value of 6^th term = 15
Hence, the median is 15.

Thus mean = 39, mode = 15 and median = 15
No, they are not same.

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 –
Arranging in increasing order, we get
32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43, 43, 45, 47, 50

(i) Mode and Median
Here, 38 and 43 occur 3 times (highest)
Thus mode = 38 and 43

n = 15(odd)
∴ Median = th term = = 8^th term
Then, value of 8^th term = 40
Hence, the median is 40.

(ii) Yes, there are 2 modes for the given weights of the students.

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
= 12, 12, 13, 13, 14, 14, 14, 16, 19
Here, 14 occur 3 times (highest)
Thus, mode = 14

n = 9 (odd)
∴ Median = th term = = 5^th term
Then, value of 5^th term = 14
Hence, the median is 14.
Hence, mode = 14 and median = 14.

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) The mode is always one of the number in a data. (True) 
(ii) The mean is one of the numbers in a data. (False)
(iii) The median is always one of the numbers in a data. (True)
(iv) The data 6, 4, 3, 8, 9, 12, 13, 9 has mean 9. (False)
Mean = (Sum of all given observations)/ (number of observations)
= = = 8
Hence, the given statement is false.