NCERT Solutions for Class 7 Maths Exercise 3.2 Chapter 3 Data Handling are available here in PDF format. This exercise of NCERT Solutions for Class 7 Maths Chapter 3 deals with mode, mode of large data and median. The mode is the value of the variable which occurs most frequently. The value of the middle-most observation is called the median of the data. Students who wish to score good marks in Maths practise NCERT Solutions for Class 7 Chapter 3.
NCERT Solutions for Class 7 Maths Chapter 3 Data Handling – Exercise 3.2
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Access Answers to Maths NCERT Solutions for Class 7 Chapter 3 – Data Handling Exercise 3.2
1. The scores in the Mathematics test (out of 25) of 15 students are 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 the same?
Solution:-
Arranging the given scores in ascending order, we get
5, 9, 10, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25, 25
Mode
Mode is the value of the variable which occurs most frequently.
Clearly, 20 occurs the maximum number of times.
Hence, the mode of the given sores is 20
Median,
The value of the middle-most observation is called the median of the data.
Here, n = 15, which is odd.
Where n is the number of students.
∴ median = value of ½ (n + 1)th observation
= ½ (15 + 1)
= ½ (16)
= 16/2
= 8
Then, the value of the 8th term = 20
Hence, the median is 20.
Yes, both values are the same.
2. The runs scored in a cricket match by 11 players are 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 runs scored in a cricket match by 11 players in ascending order, we get
6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120
Mean
Mean of the given data = Sum of all observations/Total number of observations
= (6 + 8 + 10 + 10 + 15 + 15 + 15 + 50 + 80 + 100 + 120)/ 11
= 429/11
= 39
Mode
Mode is the value of the variable which occurs most frequently.
Clearly, 15 occurs the maximum number of times.
Hence, the mode of the given sores is 15.
Median,
The value of the middle-most observation is called the median of the data.
Here, n = 11, which is odd.
Where n is the number of players.
∴ median = value of ½ (n + 1)th observation
= ½ (11 + 1)
= ½ (12)
= 12/2
= 6
Then, the value of the 6th term = 15
Hence, the median is 15.
No, these three are not the same.
3. The weights (in kg.) of 15 students in 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 the given weights of 15 students of a class in ascending order, we get
32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43, 43, 45, 47, 50
(i) Mode and Median
Mode
Mode is the value of the variable which occurs most frequently.
Clearly, 38 and 43 both occur 3 times.
Hence, the mode of the given weights is 38 and 43.
Median
The value of the middle-most observation is called the median of the data.
Here, n = 15, which is odd.
Where n is the number of students.
∴ median = value of ½ (n + 1)th observation
= ½ (15 + 1)
= ½ (16)
= 16/2
= 8
Then, the value of the 8th 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 ascending order, we get
= 12, 12, 13, 13, 14, 14, 14, 16, 19
Mode
Mode is the value of the variable which occurs most frequently.
Clearly, 14 occurs the maximum number of times.
Hence, the mode of the given data is 14.
Median
The value of the middle-most observation is called the median of the data.
Here n = 9, which is odd.
Where n is the number of students.
∴ median = value of ½ (9 + 1)th observation
= ½ (9 + 1)
= ½ (10)
= 10/2
= 5
Then, the value of the 5th term = 14
Hence, the median is 14.
5. Tell whether the statement is true or false:
(i) The mode is always one of the numbers in a data.
Solution:-
The statement given above is true.
Because mode is the value of the variable which occurs most frequently in the given data.
Hence, the mode is always one of the numbers in the data.
(ii) The mean is one of the numbers in a data.
Solution:-
The statement given above is false.
Because mean may or may not be one of the numbers in a data.
(iii) The median is always one of the numbers in a data.
Solution:-
The statement given above is true.
Because the median is the value of the middle-most observation in the given data while arranged in ascending or descending order.
Hence, the median is always one of the numbers in a data
(iv) The data 6, 4, 3, 8, 9, 12, 13, 9 have a mean 9.
Solution:-
Mean = Sum of all given observations/ number of observations
= (6 + 4 + 3 + 8 + 9 + 12 + 13 + 9)/8
= (64/8)
= 8
Hence, the given statement is false.
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