NCERT Solutions for Class 7 Maths Chapter 3 Data Handling
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Book Name: Maths
Subject: Maths
Chapter Number: 3
Chapter Name: Data Handling
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Book Name: Maths
Subject: Maths
Chapter Number: 3
Chapter Name: Data Handling
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Page 1
NCERT
SOLUTIONS
CLASS - 7TH
aglase .co
SOLUTIONS
CLASS - 7TH
aglase .co
Page 2
Book : Mathematics Ncert Solutions | Chapter-3 Maths
Class : 7th
Subject : Maths
Chapter : 3
Chapter Name : Data Handling
Exercise 3.1
Q1 Find the range of heights of any ten students of your class.
Answer. Let the heights (in cm) of 10 students of our class be 125, 127, 132, 133, 134, 136,138, 141,
144, 146
Highest value among these observations = 146
Lowest value among these observations = 125
Range = Highest value - Lowest value
= (146 - 125) cm
= 21 cm
Page : 62 , Block Name : Exercise 3.1
Q2 Organise the following marks in a class assessment, in a tabular form.
4, 6, 7, 5, 3, 5, 4, 5, 2, 6, 2, 5, 1, 9, 6, 5, 8, 4, 6, 7
(i) Which number is the highest?
(ii) Which number is the lowest?
(iii) What is the range of the data?
(iv) Find the arithmetic mean.
Answer.
Page 1 of 11 Aglasem Schools
Class : 7th
Subject : Maths
Chapter : 3
Chapter Name : Data Handling
Exercise 3.1
Q1 Find the range of heights of any ten students of your class.
Answer. Let the heights (in cm) of 10 students of our class be 125, 127, 132, 133, 134, 136,138, 141,
144, 146
Highest value among these observations = 146
Lowest value among these observations = 125
Range = Highest value - Lowest value
= (146 - 125) cm
= 21 cm
Page : 62 , Block Name : Exercise 3.1
Q2 Organise the following marks in a class assessment, in a tabular form.
4, 6, 7, 5, 3, 5, 4, 5, 2, 6, 2, 5, 1, 9, 6, 5, 8, 4, 6, 7
(i) Which number is the highest?
(ii) Which number is the lowest?
(iii) What is the range of the data?
(iv) Find the arithmetic mean.
Answer.
Page 1 of 11 Aglasem Schools
Page 3
Book : Mathematics Ncert Solutions | Chapter-3 Maths
(i) Highest number = 9
(ii) Lowest number = 1
(iii) Range = (9 - 1) = 8
(iv) Sum of all the observations = 4 + 6 + 7 + 5 + 3 + 5 + 4 + 5 + 2 + 6 + 2 +5 + 1 + 9 + 6 + 5 + 8 + 4 + 6 + 7
= 100
Total number of observations = 20
Sum of all the observations
Arithmetic mean = = 100
20
=5
Total number of the observations
Page : 62 , Block Name : Exercise 3.1
Q3 Find the mean of the rst ve whole numbers.
Answer. First ve whole numbers are 0, 1, 2, 3, and 4.
Mean = = =2
0+1+2+3+4 10
5 5
Therefore, the mean of rst ve whole numbers is 2.
Page : 62 , Block Name : Exercise 3.1
Q4 A cricketer scores the following runs in eight innings:
58, 76, 40, 35, 46, 45, 0, 100.
Find the mean score.
Answer. Runs scored by the cricketer are 58, 76, 40, 35, 46, 45, 0, and 100.
Total runs scored in all the innings
Mean score = Total number of the innings
Mean score = = =50
58+76+40+35+46+45+0+100 400
8 8
Therefore, mean score is 50.
Page : 62 , Block Name : Exercise 3.1
Q5 Following table shows the points of each player scored in four games:
Now answer the following questions:
(i) Find the mean to determine A’s average number of points scored per game.
(ii) To nd the mean number of points per game for C, would you divide the total points by 3 or by 4?
Why?
(iii) B played in all the four games. How would you nd the mean?
(iv) Who is the best performer?
Answer. (i) A's average number of points = = = 12.5
14+16+10+10 50
4 4
(ii) To nd the mean number of points per game for C, we will divide the total points by 3 because C
Page 2 of 11 Aglasem Schools
(i) Highest number = 9
(ii) Lowest number = 1
(iii) Range = (9 - 1) = 8
(iv) Sum of all the observations = 4 + 6 + 7 + 5 + 3 + 5 + 4 + 5 + 2 + 6 + 2 +5 + 1 + 9 + 6 + 5 + 8 + 4 + 6 + 7
= 100
Total number of observations = 20
Sum of all the observations
Arithmetic mean = = 100
20
=5
Total number of the observations
Page : 62 , Block Name : Exercise 3.1
Q3 Find the mean of the rst ve whole numbers.
Answer. First ve whole numbers are 0, 1, 2, 3, and 4.
Mean = = =2
0+1+2+3+4 10
5 5
Therefore, the mean of rst ve whole numbers is 2.
Page : 62 , Block Name : Exercise 3.1
Q4 A cricketer scores the following runs in eight innings:
58, 76, 40, 35, 46, 45, 0, 100.
Find the mean score.
Answer. Runs scored by the cricketer are 58, 76, 40, 35, 46, 45, 0, and 100.
Total runs scored in all the innings
Mean score = Total number of the innings
Mean score = = =50
58+76+40+35+46+45+0+100 400
8 8
Therefore, mean score is 50.
Page : 62 , Block Name : Exercise 3.1
Q5 Following table shows the points of each player scored in four games:
Now answer the following questions:
(i) Find the mean to determine A’s average number of points scored per game.
(ii) To nd the mean number of points per game for C, would you divide the total points by 3 or by 4?
Why?
(iii) B played in all the four games. How would you nd the mean?
(iv) Who is the best performer?
Answer. (i) A's average number of points = = = 12.5
14+16+10+10 50
4 4
(ii) To nd the mean number of points per game for C, we will divide the total points by 3 because C
Page 2 of 11 Aglasem Schools
Page 4
Book : Mathematics Ncert Solutions | Chapter-3 Maths
played 3 games.
(iii) Mean’s of B’s Score = = = 4.5
0+8+6+4 18
4 4
(iv) The best performer will have the greatest average among all. Now we can observe that the
average of A is 12.5 which is more than that of B and C. Therefore, A is the
best performer among these three.
Page : 63 , Block Name : Exercise 3.1
Q6 The marks (out of 100) obtained by a group of students in a science test are 85, 76, 90, 85, 39, 48,
56, 95, 81 and 75. Find the:
(i) Highest and the lowest marks obtained by the students.
(ii) Range of the marks obtained.
(iii) Mean marks obtained by the group.
Answer. The marks obtained by the group of students in a science test can be arranged in an
ascending order as follows.
39, 48, 56, 75, 76, 81, 85, 85, 90, 95
(i) Highest marks = 95
Lowest marks = 39
(ii) Range = 95 − 39 = 56
(85+76+90+85+39+48+56+95+81+75)
(iii) Mean Marks = 10
= 730
10
= 73
Page : 63 , Block Name : Exercise 3.1
Q7 The enrolment in a school during six consecutive years was as follows:
1555, 1670, 1750, 2013, 2540, 2820
Find the mean enrolment of the school for this period.
(1555+1670+1750+2013+2540+2820)
Answer. Mean enrollment = = = 2058
12348
6 6
Page : 63 , Block Name : Exercise 3.1
Q8 The rainfall (in mm) in a city on 7 days of a certain week was recorded as follows:
(i) Find the range of the rainfall in the above data.
(ii) Find the mean rainfall for the week.
(iii) On how many days was the rainfall less than the mean rainfall.
Answer. (i) Range = (20.5 − 0.0) mm= 20.5 mm
(0.0+12.2+2.1+0.0+20.5+5.5+1.0)
(ii) Mean rainfall = = = 5.9 mm
41.3
7 7
(iii) For 5 days (i.e., Monday, Wednesday, Thursday, Saturday, Sunday), the rainfall was less than the
average rainfall.
Page : 63 , Block Name : Exercise 3.1
Page 3 of 11 Aglasem Schools
played 3 games.
(iii) Mean’s of B’s Score = = = 4.5
0+8+6+4 18
4 4
(iv) The best performer will have the greatest average among all. Now we can observe that the
average of A is 12.5 which is more than that of B and C. Therefore, A is the
best performer among these three.
Page : 63 , Block Name : Exercise 3.1
Q6 The marks (out of 100) obtained by a group of students in a science test are 85, 76, 90, 85, 39, 48,
56, 95, 81 and 75. Find the:
(i) Highest and the lowest marks obtained by the students.
(ii) Range of the marks obtained.
(iii) Mean marks obtained by the group.
Answer. The marks obtained by the group of students in a science test can be arranged in an
ascending order as follows.
39, 48, 56, 75, 76, 81, 85, 85, 90, 95
(i) Highest marks = 95
Lowest marks = 39
(ii) Range = 95 − 39 = 56
(85+76+90+85+39+48+56+95+81+75)
(iii) Mean Marks = 10
= 730
10
= 73
Page : 63 , Block Name : Exercise 3.1
Q7 The enrolment in a school during six consecutive years was as follows:
1555, 1670, 1750, 2013, 2540, 2820
Find the mean enrolment of the school for this period.
(1555+1670+1750+2013+2540+2820)
Answer. Mean enrollment = = = 2058
12348
6 6
Page : 63 , Block Name : Exercise 3.1
Q8 The rainfall (in mm) in a city on 7 days of a certain week was recorded as follows:
(i) Find the range of the rainfall in the above data.
(ii) Find the mean rainfall for the week.
(iii) On how many days was the rainfall less than the mean rainfall.
Answer. (i) Range = (20.5 − 0.0) mm= 20.5 mm
(0.0+12.2+2.1+0.0+20.5+5.5+1.0)
(ii) Mean rainfall = = = 5.9 mm
41.3
7 7
(iii) For 5 days (i.e., Monday, Wednesday, Thursday, Saturday, Sunday), the rainfall was less than the
average rainfall.
Page : 63 , Block Name : Exercise 3.1
Page 3 of 11 Aglasem Schools
Page 5
Book : Mathematics Ncert Solutions | Chapter-3 Maths
Q9 The heights of 10 girls were measured in cm and the results are as follows: 135, 150, 139, 128,
151, 132, 146, 149, 143, 141.
(i) What is the height of the tallest girl?
(ii) What is the height of the shortest girl?
(iii) What is the range of the data?
(iv) What is the mean height of the girls?
(v) How many girls have heights more than the mean height.
Answer. Arranging the heights of 10 girls in an ascending order,
128, 132, 135, 139, 141, 143, 146, 149, 150, 151
(i) Height of the tallest girl = 151 cm
(ii) Height of the shortest girl = 128 cm
(iii) Range = (151 − 128) cm= 23 cm
(135+150+139+128+151+132+146+149+143+141)
(iv) Mean Height = 10
= 1414
10
= 141.4 cm
(v) The heights of 5 girls are greater than the mean height (i.e., 141.4 cm) and these heights are 143,
146, 149, 150, and 151 cm.
Page : 63 , Block Name : Exercise 3.1
Exercise 3.2
Q1 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?
Answer. Scores of 15 students in mathematics test are 19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24,
12, 20
Arranging these scores in an ascending order, 5, 9, 10, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25, 25
Mode of a given data is that value of observation which occurs for the most number of times. Median
of a given data is the middle observation when the data is arranged in an ascending or descending
order.
As there are 15 terms in the given data, therefore, the median of this data will be the 8th
observation.
Hence, median = 20
Also, it can be observed that 20 occurs 4 times (i.e., maximum number of times).
Therefore, mode of this data = 20
Yes, both are same.
Page : 68 , Block Name : Exercise 3.2
Q2 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?
Page 4 of 11 Aglasem Schools
Q9 The heights of 10 girls were measured in cm and the results are as follows: 135, 150, 139, 128,
151, 132, 146, 149, 143, 141.
(i) What is the height of the tallest girl?
(ii) What is the height of the shortest girl?
(iii) What is the range of the data?
(iv) What is the mean height of the girls?
(v) How many girls have heights more than the mean height.
Answer. Arranging the heights of 10 girls in an ascending order,
128, 132, 135, 139, 141, 143, 146, 149, 150, 151
(i) Height of the tallest girl = 151 cm
(ii) Height of the shortest girl = 128 cm
(iii) Range = (151 − 128) cm= 23 cm
(135+150+139+128+151+132+146+149+143+141)
(iv) Mean Height = 10
= 1414
10
= 141.4 cm
(v) The heights of 5 girls are greater than the mean height (i.e., 141.4 cm) and these heights are 143,
146, 149, 150, and 151 cm.
Page : 63 , Block Name : Exercise 3.1
Exercise 3.2
Q1 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?
Answer. Scores of 15 students in mathematics test are 19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24,
12, 20
Arranging these scores in an ascending order, 5, 9, 10, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25, 25
Mode of a given data is that value of observation which occurs for the most number of times. Median
of a given data is the middle observation when the data is arranged in an ascending or descending
order.
As there are 15 terms in the given data, therefore, the median of this data will be the 8th
observation.
Hence, median = 20
Also, it can be observed that 20 occurs 4 times (i.e., maximum number of times).
Therefore, mode of this data = 20
Yes, both are same.
Page : 68 , Block Name : Exercise 3.2
Q2 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?
Page 4 of 11 Aglasem Schools
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Book : Mathematics Ncert Solutions | Chapter-3 Maths
Answer. The runs scored by 11 players are 6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15
Arranging these scores in an ascending order, 6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120
Mean=
6+8+10+10+15+15+15+50+80+100+120
11
Mode of a given data is that value of observation which occurs for the most number of times and the
median of the given data is the middle observation when the data is arranged in an ascending or
descending order.
As there are 11 terms in the given data, therefore, the median of this data will be the 6th
observation.
Median = 15
Also, it can be observed that 15 occurs 3 times (i.e., maximum number of times).
Therefore, mode of this data = 15
No, these three are not same.
Page : 68 , Block Name : Exercise 3.2
Q3 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?
Answer. The weights of 15 students are 38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47
Arranging these weights in ascending order, 32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43, 43, 45, 47, 50
(i) Mode of a given data is that value of observation which occurs for the most number of times and
the median of the given data is the middle observation when the data is arranged in an ascending or
descending order.
As there are 15 terms in the given data, therefore, the median of this data will be the 8th
observation.
Hence, median 40
Also, it can be observed that 38 and 43 both occur 3 times (i.e., maximum number of times).
Therefore, mode of this data 38 and 43.
(ii) Yes, there are 2 modes for the given data.
Page : 68 , Block Name : Exercise 3.2
Q4 Find the mode and median of the data:
13, 16, 12, 14, 19, 12, 14, 13, 14
Answer. The given data is 13, 16, 12, 14, 19, 12, 14, 13, 14
Arranging the given data in an ascending order, 12, 12, 13, 13, 14, 14, 14, 16, 19
Mode of a given data is that value of observation Which occurs for the most number of times and the
median of the given data is the middle observation when the data iS arranged in an ascending or
descending order.
As there are 9 terms in the given data, therefore, the median of this data Will be the 5th observation.
Hence, median 14
Also, it can be observed that 14 occurs 3 times (i.e., maximum number of times).
Therefore, mode of this data = 14
Page 5 of 11 Aglasem Schools
Answer. The runs scored by 11 players are 6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15
Arranging these scores in an ascending order, 6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120
Mean=
6+8+10+10+15+15+15+50+80+100+120
11
Mode of a given data is that value of observation which occurs for the most number of times and the
median of the given data is the middle observation when the data is arranged in an ascending or
descending order.
As there are 11 terms in the given data, therefore, the median of this data will be the 6th
observation.
Median = 15
Also, it can be observed that 15 occurs 3 times (i.e., maximum number of times).
Therefore, mode of this data = 15
No, these three are not same.
Page : 68 , Block Name : Exercise 3.2
Q3 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?
Answer. The weights of 15 students are 38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47
Arranging these weights in ascending order, 32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43, 43, 45, 47, 50
(i) Mode of a given data is that value of observation which occurs for the most number of times and
the median of the given data is the middle observation when the data is arranged in an ascending or
descending order.
As there are 15 terms in the given data, therefore, the median of this data will be the 8th
observation.
Hence, median 40
Also, it can be observed that 38 and 43 both occur 3 times (i.e., maximum number of times).
Therefore, mode of this data 38 and 43.
(ii) Yes, there are 2 modes for the given data.
Page : 68 , Block Name : Exercise 3.2
Q4 Find the mode and median of the data:
13, 16, 12, 14, 19, 12, 14, 13, 14
Answer. The given data is 13, 16, 12, 14, 19, 12, 14, 13, 14
Arranging the given data in an ascending order, 12, 12, 13, 13, 14, 14, 14, 16, 19
Mode of a given data is that value of observation Which occurs for the most number of times and the
median of the given data is the middle observation when the data iS arranged in an ascending or
descending order.
As there are 9 terms in the given data, therefore, the median of this data Will be the 5th observation.
Hence, median 14
Also, it can be observed that 14 occurs 3 times (i.e., maximum number of times).
Therefore, mode of this data = 14
Page 5 of 11 Aglasem Schools
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Book : Mathematics Ncert Solutions | Chapter-3 Maths
Page : 68 , Block Name : Exercise 3.2
Q5 Tell whether the statement is true or false:
(i) The mode is always one of the numbers 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.
Answer. (i) True
Mode of a given data is that value of observation which occurs for the most number of times.
Therefore, it is one of the observations given in the data.
(ii) False
Mean may or may not be one of the numbers in the data.
(iii) True
The median of the given data is the middle observation when the data is arranged in an ascending or
descending order.
(iv) False
The given data is 6, 4, 3, 8, 9, 12, 13, 9
Mean = =8
6+4+3+8+9+12+13+9 64
=
8 8
Page : 68 , Block Name : Exercise 3.2
Exercise 3.3
Q1 Use the bar graph to answer the following questions.
(a) Which is the most popular pet?
(b) How many students have dog as a pet?
Answer. (a) Since the bar representing cats is the tallest, cat is the most popular pet.
(b) The number of children having dog as a pet are 8.
Page : 72 , Block Name : Exercise 3.3
Q2 Read the bar graph which shows the number of books sold by a bookstore during ve consecutive
years and answer the following questions:
Page 6 of 11 Aglasem Schools
Page : 68 , Block Name : Exercise 3.2
Q5 Tell whether the statement is true or false:
(i) The mode is always one of the numbers 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.
Answer. (i) True
Mode of a given data is that value of observation which occurs for the most number of times.
Therefore, it is one of the observations given in the data.
(ii) False
Mean may or may not be one of the numbers in the data.
(iii) True
The median of the given data is the middle observation when the data is arranged in an ascending or
descending order.
(iv) False
The given data is 6, 4, 3, 8, 9, 12, 13, 9
Mean = =8
6+4+3+8+9+12+13+9 64
=
8 8
Page : 68 , Block Name : Exercise 3.2
Exercise 3.3
Q1 Use the bar graph to answer the following questions.
(a) Which is the most popular pet?
(b) How many students have dog as a pet?
Answer. (a) Since the bar representing cats is the tallest, cat is the most popular pet.
(b) The number of children having dog as a pet are 8.
Page : 72 , Block Name : Exercise 3.3
Q2 Read the bar graph which shows the number of books sold by a bookstore during ve consecutive
years and answer the following questions:
Page 6 of 11 Aglasem Schools
Page 8
Book : Mathematics Ncert Solutions | Chapter-3 Maths
(i) About how many books were sold in 1989? 1990? 1992?
(ii) In which year were about 475 books sold? About 225 books sold?
(iii) In which years were fewer than 250 books sold?
(iv) Can you explain how you would estimate the number of books sold in 1989?
Answer. (i) In 1989, 175 books were sold. In 1990, 475 books were sold. In 1992, 225 books were sold.
(ii) From the graph, it can be concluded that 475 books were sold in the year 1990 and 225 books
were sold in the year 1992.
(iii) From the graph, it can be concluded that in the years 1989 and 1992, the number of books sold
were less than 250.
(iv) From the graph, it can be concluded that the number of books sold in the year 1989 is about 1
and th part of 1 cm.
3
4
We know that the scale is taken as 1 cm = 100 books
× 100 = 100 + 75 = 175
3
100 +
4
Therefore, about 175 books were sold in the year 1989.
Page : 72 , Block Name : Exercise 3.3
Q3 Number of children in six different classes are given below. Represent the data on a bar graph.
(a) How would you choose a scale?
(b) Answer the following questions:
(i) Which class has the maximum number of children? And the minimum?
(ii) Find the ratio of students of class sixth to the students of class eight.
Answer.
(a) We will choose a scale as 1 unit 10 children because we can represent a more
Page 7 of 11 Aglasem Schools
(i) About how many books were sold in 1989? 1990? 1992?
(ii) In which year were about 475 books sold? About 225 books sold?
(iii) In which years were fewer than 250 books sold?
(iv) Can you explain how you would estimate the number of books sold in 1989?
Answer. (i) In 1989, 175 books were sold. In 1990, 475 books were sold. In 1992, 225 books were sold.
(ii) From the graph, it can be concluded that 475 books were sold in the year 1990 and 225 books
were sold in the year 1992.
(iii) From the graph, it can be concluded that in the years 1989 and 1992, the number of books sold
were less than 250.
(iv) From the graph, it can be concluded that the number of books sold in the year 1989 is about 1
and th part of 1 cm.
3
4
We know that the scale is taken as 1 cm = 100 books
× 100 = 100 + 75 = 175
3
100 +
4
Therefore, about 175 books were sold in the year 1989.
Page : 72 , Block Name : Exercise 3.3
Q3 Number of children in six different classes are given below. Represent the data on a bar graph.
(a) How would you choose a scale?
(b) Answer the following questions:
(i) Which class has the maximum number of children? And the minimum?
(ii) Find the ratio of students of class sixth to the students of class eight.
Answer.
(a) We will choose a scale as 1 unit 10 children because we can represent a more
Page 7 of 11 Aglasem Schools
Page 9
Book : Mathematics Ncert Solutions | Chapter-3 Maths
clear difference between the number of students of class 7th and that of class 9th by this scale.
(b)
(i) Since the bar representing the number of children for class fth is the tallest, there are maximum
number of children in class fth. Similarly, since the bar representing the number of children for
class tenth is the smallest, there are minimum number of children in class tenth.
(ii) The number of students in class sixth is 120 and the number of students in class eighth is 100.
Therefore, the ratio between the number of students of class sixth and the number of students of
class eighth =120
100
=
6
5
= 6 : 5
Page : 73 , Block Name : Exercise 3.3
Q4 The performance of a student in 1st Term and 2nd Term is given. Draw a double bar graph
choosing appropriate scale and answer the following:
(i) In which subject, has the child improved his performance the most?
(ii) In which subject is the improvement the least?
(iii) Has the performance gone down in any subject?
Answer. A double bar graph for the given data is as follows.
(i) There was a maximum increase in the marks obtained in Maths. Therefore, the child has improved
his performance the most in Maths.
(ii) From the graph, it can be concluded that the improvement was the least in S.Science.
(iii) From the graph, it can be observed that the performance in Hindi has gone down.
Page : 73 , Block Name : Exercise 3.3
Q5 Consider this data collected from a survey of a colony.
Page 8 of 11 Aglasem Schools
clear difference between the number of students of class 7th and that of class 9th by this scale.
(b)
(i) Since the bar representing the number of children for class fth is the tallest, there are maximum
number of children in class fth. Similarly, since the bar representing the number of children for
class tenth is the smallest, there are minimum number of children in class tenth.
(ii) The number of students in class sixth is 120 and the number of students in class eighth is 100.
Therefore, the ratio between the number of students of class sixth and the number of students of
class eighth =120
100
=
6
5
= 6 : 5
Page : 73 , Block Name : Exercise 3.3
Q4 The performance of a student in 1st Term and 2nd Term is given. Draw a double bar graph
choosing appropriate scale and answer the following:
(i) In which subject, has the child improved his performance the most?
(ii) In which subject is the improvement the least?
(iii) Has the performance gone down in any subject?
Answer. A double bar graph for the given data is as follows.
(i) There was a maximum increase in the marks obtained in Maths. Therefore, the child has improved
his performance the most in Maths.
(ii) From the graph, it can be concluded that the improvement was the least in S.Science.
(iii) From the graph, it can be observed that the performance in Hindi has gone down.
Page : 73 , Block Name : Exercise 3.3
Q5 Consider this data collected from a survey of a colony.
Page 8 of 11 Aglasem Schools
Page 10
Book : Mathematics Ncert Solutions | Chapter-3 Maths
(i) Draw a double bar graph choosing an appropriate scale. What do you infer from the bar graph?
(ii) Which sport is most popular?
(iii) Which is more preferred, watching or participating in sports?
Answer. (i) A double bar graph for the given data is as follows.
The double bar graph represents the number of people who like watching and participating in
different sports. It can be observed that most of the people like watching and participating in cricket
while the least number of people like watching and participating in athletics.
(ii) From the bar graph, it can be observed that the bar representing the number of people who like
watching and participating in cricket is the tallest among all the bars. Hence, cricket is the most
popular sport.
(iii) The bars representing watching sport are longer than the bars representing participating in
sport. Hence, watching different types of sports is more preferred than participating in the sports.
Page : 73 , Block Name : Exercise 3.3
Q6 Take the data giving the minimum and the maximum temperature of various cities given in the
beginning of this chapter. Plot a double bar graph using the data and answer the following:
Page 9 of 11 Aglasem Schools
(i) Draw a double bar graph choosing an appropriate scale. What do you infer from the bar graph?
(ii) Which sport is most popular?
(iii) Which is more preferred, watching or participating in sports?
Answer. (i) A double bar graph for the given data is as follows.
The double bar graph represents the number of people who like watching and participating in
different sports. It can be observed that most of the people like watching and participating in cricket
while the least number of people like watching and participating in athletics.
(ii) From the bar graph, it can be observed that the bar representing the number of people who like
watching and participating in cricket is the tallest among all the bars. Hence, cricket is the most
popular sport.
(iii) The bars representing watching sport are longer than the bars representing participating in
sport. Hence, watching different types of sports is more preferred than participating in the sports.
Page : 73 , Block Name : Exercise 3.3
Q6 Take the data giving the minimum and the maximum temperature of various cities given in the
beginning of this chapter. Plot a double bar graph using the data and answer the following:
Page 9 of 11 Aglasem Schools
Page 11
Book : Mathematics Ncert Solutions | Chapter-3 Maths
(i) Which city has the largest difference in the minimum and maximum temperature on the given
date?
(ii) Which is the hottest city and which is the coldest city?
(iii) Name two cities where maximum temperature of one was less than the minimum temperature of
the other.
(iv) Name the city which has the least difference between its minimum and the maximum
temperature.
Answer. A double bar graph for the given data is constructed as follows.
(i) From the graph, it can be concluded that Jammu has the largest difference in its minimum and
maximum temperatures on 20.6.2006.
(ii) From the graph, it can be concluded that Jammu is the hottest city and Bangalore is the coldest
city.
(iii) Bangalore and Jaipur, Bangalore and Ahmedabad
For Bangalore, the maximum temperature was 280C, while minimum temperature of both cities,
Ahmedabad and Jaipur, was 290C.
(iv) From the graph, it can be concluded that the city which has the least difference between its
minimum and maximum temperatures is Mumbai.
Page 10 of 11 Aglasem Schools
(i) Which city has the largest difference in the minimum and maximum temperature on the given
date?
(ii) Which is the hottest city and which is the coldest city?
(iii) Name two cities where maximum temperature of one was less than the minimum temperature of
the other.
(iv) Name the city which has the least difference between its minimum and the maximum
temperature.
Answer. A double bar graph for the given data is constructed as follows.
(i) From the graph, it can be concluded that Jammu has the largest difference in its minimum and
maximum temperatures on 20.6.2006.
(ii) From the graph, it can be concluded that Jammu is the hottest city and Bangalore is the coldest
city.
(iii) Bangalore and Jaipur, Bangalore and Ahmedabad
For Bangalore, the maximum temperature was 280C, while minimum temperature of both cities,
Ahmedabad and Jaipur, was 290C.
(iv) From the graph, it can be concluded that the city which has the least difference between its
minimum and maximum temperatures is Mumbai.
Page 10 of 11 Aglasem Schools
Page 12
Book : Mathematics Ncert Solutions | Chapter-3 Maths
Page : 73 , Block Name : Exercise 3.3
Exercise 3.4
Q1 Tell whether the following is certain to happen, impossible, can happen but not certain.
(i) You are older today than yesterday.
(ii) A tossed coin will land heads up.
(iii) A die when tossed shall land up with 8 on top.
(iv) The next traf c light seen will be green.
(v) Tomorrow will be a cloudy day.
Answer. (i) Certain
(ii) Can happen but not certain
(iii) Impossible as there are only six faces on a dice marked as 1, 2, 3, 4, 5, 6 on it.
(iv) Can happen but not certain
(v) Can happen but not certain
Page : 76 , Block Name : Exercise 3.4
Q2 There are 6 marbles in a box with numbers from 1 to 6 marked on each of them.
(i) What is the probability of drawing a marble with number 2?
(ii) What is the probability of drawing a marble with number 5?
Number of favourable outcomes
Answer. (i) Probability =
Number of possible outcomes
P ( appearance of 2 ) = 1
6
(ii) P ( appearance of 5 ) = 1
6
Page : 76 , Block Name : Exercise 3.4
Q3 A coin is ipped to decide which team starts the game. What is the probability that your team will
start?
Answer. A coin has two faces — Head and Tail. One team can opt either Head or Tail.
Number of favourable outcomes
Probability =
Number of possible outcomes
Probability ( our team starts rst) = 1
2
Page : 76 , Block Name : Exercise 3.4
Page 11 of 11 Aglasem Schools
Page : 73 , Block Name : Exercise 3.3
Exercise 3.4
Q1 Tell whether the following is certain to happen, impossible, can happen but not certain.
(i) You are older today than yesterday.
(ii) A tossed coin will land heads up.
(iii) A die when tossed shall land up with 8 on top.
(iv) The next traf c light seen will be green.
(v) Tomorrow will be a cloudy day.
Answer. (i) Certain
(ii) Can happen but not certain
(iii) Impossible as there are only six faces on a dice marked as 1, 2, 3, 4, 5, 6 on it.
(iv) Can happen but not certain
(v) Can happen but not certain
Page : 76 , Block Name : Exercise 3.4
Q2 There are 6 marbles in a box with numbers from 1 to 6 marked on each of them.
(i) What is the probability of drawing a marble with number 2?
(ii) What is the probability of drawing a marble with number 5?
Number of favourable outcomes
Answer. (i) Probability =
Number of possible outcomes
P ( appearance of 2 ) = 1
6
(ii) P ( appearance of 5 ) = 1
6
Page : 76 , Block Name : Exercise 3.4
Q3 A coin is ipped to decide which team starts the game. What is the probability that your team will
start?
Answer. A coin has two faces — Head and Tail. One team can opt either Head or Tail.
Number of favourable outcomes
Probability =
Number of possible outcomes
Probability ( our team starts rst) = 1
2
Page : 76 , Block Name : Exercise 3.4
Page 11 of 11 Aglasem Schools
Document Details
| Board / Org | NCERT |
| Exam | Class 7 |
| Type | Solution |
| Pages | 12 |
| Updated | 30 Apr 2026 |