NCERT Solutions for Class 7 Maths Chapter 3 Data Handling

NCERT Solutions for Class 7 Maths Chapter 3 Data Handling, are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 3 Data Handling.

NCERT Solutions for Class 7 Maths Chapter 3 Data Handling

NCERT Solutions for Class 7 Maths Chapter 3 Data Handling Ex 3.1

Question 1.
Find the range of heights of any ten students of your class.
Solution:
Please try yourself.

Question 2.
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.
Solution:

(i) Highest number is 9.
(ii) Lowest number is 1.
(iii) Range of the data = Highest observation – Lowest observation
= 9 – 1 = 8

Question 3.
Find the mean of first five whole numbers.
Solution:
First 5 whole numbers are 0, 1, 2, 3 and 4.
Their arithmetic mean

Question 4.
A cricketer scores the following runs in eight innings:
58, 76, 40, 35, 46, 45, 0, 100.
Find the mean score.
Solution:

Question 5.
Following table shows the points of each player scored in four games:

Now answer the following questions:

1. Find the mean to determine A’s average number of points scored per game.
2. To find the mean number of points per game for C, would you divide the total points by 3 or by 4? Why?
3. B played in all the four games. How would you find the mean?
4. Who is the best performer?

Solution:

So, A’s average number of points scored per game is 12.5.
(ii) To find the mean number of points per game for C, we shall divide the total points by 3 because the number of games under consideration is 4 but ‘C’ did not play game 3.

Question 6.
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:

1. Highest and the lowest marks obtained by the students.
2. Range of the marks obtained.
3. Mean marks obtained by the group.

Solution:

1. Highest marks obtained by the students = 95
   Lowest marks obtained by the students = 39
2. Range of the marks obtained = Highest marks – Lowest marks = 95 – 39 = 56
3. Mean marks obtained by the group
   

Question 7.
The enrolment of 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.
Solution:
Mean enrolment of the school for this period.

Question 8.
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?
Solution:
(i) Range of the rainfall
= Highest rainfall – Lowest rainfall = 20.5 mm – 0.0 mm = 20.5 mm
(ii) Mean rainfall for the week

(iii) The rainfall was less than the mean rainfall on 5 days.

Question 9.
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.

1. What is the height of the tallest girl ?
2. What is the height of the shortest girl?
3. What is the range of the data?
4. What is the mean height of the girls?
5. How many girls have heights more than the mean height?

Solution:
(i) Height of the tallest girl = 151 cm
(ii) Height of the shortest girl = 128 cm
(iii) Range of the data

(v) 5 girls have heights more than the mean height.

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

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:
For Median. We arrange the data in ascending order, we get
5, 9, 10, 12, 15, 16, 19, 20,
20, 20, 20, 23, 24, 25, 25
Median is the middle observation.
Therefore, 20 is the median.
For Mode.
Mode
= Observation with highest frequency = 20
Yes ! they are same.

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:

(ii) For Median. We arrange the data in ascending order, we get
6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120
Median is the middle observation. Therefore, 15 is the median.
(iii) For Mode. Mode = observation with highest frequency = 15
No ! They are not the same.

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

1. Find the mode and median of this data.
2. Is there more than one mode?

Solution:
(i) For Median. We arrange the data in ascending order, we get
32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43,
43, 45, 47, 50
Median is the middle observation.
Therefore, 40 kg is the median.
For Mode. Mode = observation with highest frequency = 38 kg and 43 kg.
(ii) Yes ! there are 2 (more than one) modes.

Question 4.
Find the mode and median of the data:
13, 16, 12, 14, 19, 12, 14, 13, 14.
Solution:
For Median. We arrange the data in ascending order, we get 12, 12, 13, 13, 14, 14, 14, 16, 19.
Median is the middle observation.
Therefore, 14 is the median.
For Mode. Mode = observation with highest frequency = 14.

Question 5.
Tell whether the statement is true or false:

1. The mode is always one of the numbers in a data.
2. The mean is one of the numbers in a data.
3. The median is always one of the numbers in a data.
4. The data 6, 4, 3, 8, 9, 12, 13, 9 has mean 9.

Solution:

1. True
2. False
3. True
4. False.

NCERT Solutions for Class 7 Maths Chapter 3 Data Handling Ex 3.3

Question 1.
Use the bar graph to answer the following questions.
(a) Which is the most popular pet?
(b) How many children have dog as a pet?

Solution:
(a) The most popular pet is ‘Cat’.
(b) 8 children have a dog as a pet.

Question 2.
Read the bar graph which shows the number of books sold by a bookstore during five consecutive years and answer the following questions:

1. About how many books were sold in 1989?1990?1992?
2. ln which year were about 475 books sold? About 225 books sold?
3. In which years were fewer than 250 books sold?
4. Can you explain how you would estimate the number of books sold in 1989?

Solution:

1. Number of books sold in 1989 = 175 (approx.)
   Number of books sold in 1990 = 475 (approx.)
   Number of books sold in 1992 = 225 (approx.)
2. About 475 were sold in the year 1990. About 225 books were sold in the year 1992.
3. Fewer than 250 books were sold in the years 1989 and 1992.
4. Length of the bar corresponding to 1989 is about 1.75 cm. The scale is 1 cm = 100 books. So, the number of books estimated to be sold in 1989 = 1.75 × 100 = 175.

Question 3.
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 eighth.
Solution:

(a) Start the scale at 0. The greatest value in the data is 135, so end the scale at a value greater than 135, such as 140. Use equal divisions along the axes, such as increments of 10.
We know that all the bars would lie between 0 and 140.
We choose the scale such that the length between 0 and 140 is neither too long nor too small.
Here, we take 1 unit for 10 children.
(b) (i) Fifth class has the maximum number of children. Tenth class has the minimum number of children.
(ii) Ratio of students of class sixth to eighth
= 120 : 100 = \(\frac { 12 }{ 100 } \) = \(\frac { 6 }{ 5 } \) = 6 : 5

Question 4.
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 :

1. In which subject, has the child improved his performance the most?
2. In which subject is the improvement the least?
3. Has the performance gone down in any subject?

Solution:

1. The child improved his performance the most in the subject of Maths.
2. The improvement is the least in the sub :t of S. Science.
3. Yes ! The performance has gone down in the subject of Hindi.

Question 5.
Consider this data collected from a survey of a colony.

1. Draw a double graph choosing an appropriate scale.
   What do you infer from the bar graph?
2. Which sport is most popular?
3. Which is more preferred, watching or participating in sports?

Solution:

1. We infer from the bar graph that the residents of the colony like cricket, the most and athletics, the least.
2. Cricket is most popular.
3. Watching sports is preferred more than participating in sports.

Question 6.
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:

1. Which city has the largest difference in the minimum and maximum temperature on the given date? .
2. Which is the hottest city and which is the coldest city?
3. Name two cities where maximum temperature of one was less than the minimum temperature of the other.
4. Name the city which has the least difference between its minimum and the maximum temperature.

Solution:


Jammu has the largest difference in the minimum and maximum temperatures on the given date.
(ii) Jammu is the hottest city and Bangalore is the coldest city.
(iii) Bangalore and Jaipur or Bangalore andAhmedabad
(iv) Mumbai.

NCERT Solutions for Class 7 Maths Chapter 3 Data Handling Ex 3.4

Question 1.
Tell whether the following is certain to happen, impossible, can happen but not certain.

1. You are older today than yesterday.
2. A tossed coin will land heads up.
3. A die when tossed shall land up with 8 on top.
4. The next traffic light seen will be green.
5. Tomorrow will be a cloudy day.

Solution:

1. It is certain to happen
2. It can happen but not certain
3. It is impossible
4. It can happen but not certain
5. It can happen but not certain.

Question 2.
There are 6 marbles in a box with numbers from 1 to 6 marked on each of them.

1. What is the probability of drawing a marble with number 2?
2. What is the probability of drawing a marble with number 5?

Solution:

1. \(\frac { 1 }{ 6 } \)
2. \(\frac { 1 }{ 6 } \)

Question 3.
A coin is flipped to decide which team starts the game. What is the probability that your team will start?
Solution:
Probability = \(\frac { 1 }{ 2 } \)

NCERT Solutions for Class 7 Maths Chapter 3 Data Handling MCQ

Important Multiple Choice Questions

The number of tourists visiting a historical place in a week is shown in the following table :

Answer the following related questions.

1. On which day is the number of tourists maximum?

(a) Sunday
(b) Wednesday
(c) Tuesday
(d) Saturday.

2. On which day is the number of tourists minimum?

(a) Friday
(b) Monday
(c) Thursday
(d) Saturday.

3. On which day 60 tourists visit?

(a) Monday
(b) Tuesday
(c) Friday
(d) Sunday.

4. What is the difference between the num-ber of tourists visiting on Friday and Monday?

(a) 10
(b) 24
(c) 38
(d) 5.

5. The sum of the number of tourists visit-ing on Sunday and Friday is

(a) 160
(b) 60
(c) 220
(d) 100.

6. The difference between the maximum and minimum number of tourists is

(a) 50
(b) 80
(c) 90
(d) 100.

7. A batsman scored the following number of runs in six innings:
35, 30, 45, 65, 39, 20
The mean runs scored by him in an inning is

(a) 39
(b) 38
(c) 37
(d) 40.

8. The mean of the numbers 10,20, 30 and 40 is

(a) 20
(b) 25
(c) 30
(d) 50.

9. The range of the weights (in kg) of a students of a class given below is:
49, 60, 47, 50, 47, 59, 58, 45, 53

(a) 10
(b) 15
(c) 20
(d) 2.

10. The marks of 11 students of a class are as given below:
78, 11, 99, 63, 94, 6, 78, 36, 30, 55, 22
The range of marks is

(a) 90
(b) 91
(c) 92
(d) 93.

11. The rainfall (in mm) in a city on 7 days of a certain week was recorded as follows:

On how many days was the rainfall less than 6 mm?

(a) 0
(b) 3
(c) 6
(d) 7.

12. The mode of the distribution 3,5, 7, 4, 2, 1, 4, 3, 4 is

(a) 7
(b) 4
(c) 3
(d) 1.

13. The marks of some students are as given below:
30, 31, 32, 32, 33, 32, 34, 35, 30, 31, 33, 32
Find the mode of their marks.

(a) 30
(b) 31
(c) 32
(d) 33.

14. The median of the distribution 2, 3, 4, 7, 5, 1, 6 is

(a) 1
(b) 2
(c) 3
(d) 4.

15. The median of the data 20, 30, 40, 10, 15, 25, 35 is

(a) 20
(b) 25
(c) 30
(d) 40.

16. Which of the following statements is true?

(a) The mode is always one of the numbers in a data
(b) The mean is always one of the numbers in a data
(c) Mean < Mode in a data
(d) Median < Mode in a data.

17. A coin is tossed. What is the probability of getting head?

(a) 0
(b) 1
(c) \(\frac { 1 }{ 2 } \)
(d) 2

18. A coin is tossed. What is the probability of getting tail?

(a) 1
(b) \(\frac { 1 }{ 2 } \)
(c) 2
(d) 0

19. A die is thrown. What is the probability of getting 1?

(a) 0
(b) 1
(c) \(\frac { 1 }{ 2 } \)
(d) \(\frac { 1 }{ 6 } \)

20. A die is thrown. What is the probability of getting 6?

(a) 0
(b) \(\frac { 1 }{ 6 } \)
(c) \(\frac { 1 }{ 2 } \)
(d) 1

Read the following bar graph and answer the following related questions :

21. Who got the maximum marks?

(a) Apala
(b) Meenu
(c) Saroj
(d) Indu.

22. Who got the minimum marks?

(a) Apala
(b) Meenu
(c) Vimla
(d) Indu.

23. The difference between maximum and minimum marks is

(a) 100
(d) 200
(c) 400
(d) 500.

24. The ratio between the marks obtained by Saroj and Vimla is

(a) 1:2
(b) 2 : 3
(c) 3:4
(d) 1 : 6.

25. How many girls have got marks more than 100?

(a) 2
(b) 3
(c) 4
(d) 1.

26. Who has got 400 marks?

(a) Vimla
(b) Saroj
(c) Indu
(d) Apala.

27. The difference between the marks obtained by Vimla and Saroj is how many times the difference between the marks obtained by Meenu and Saroj?

(a) 2
(b) 3
(c) 4
(d) 6.

28. How many girls have got marks less than 600?

(a) 1
(b) 2
(c) 3
(d) 4

Sale of Mathematics and English books in the year 2005, 2006, 2007 and 2008 are given below :

Answer the following related questions :

29. In which year is the difference in the sale minimum?

(a)2008
(b) 2007
(c) 2006
(d) 2005.

30. In which year is the difference in the sale maximum?

(a)2005
(b) 2006
(c) 2007
(d) 2008.

31. The ratio of sales in the year 2005 is

(a) 2 : 1
(b) 3 : 1
(c) 4 : 1
(d) 2 : 3.

32. The rise in the sale of Mathematics books from 2005 to 2008 is

(a) 100
(b) 200
(c) 300
(d) 400.

33. The fall in the sale of English books from 2006 to 2007 is

(a) 50
(b) 100
(c) 150
(d) 200.

Number of children in six different classes are given below :

Answer the following related questions.

34. In which class is the number of children maximum?

(a) 6
(b) 7
(c) 8
(d) 9.

35. In which class is the number of children minimum?

(a) 8
(b) 9
(c) 10
(d) 11.

36. The difference between the maximum and minimum number of children is

(a) 100
(b) 200
(c) 300
(d) 400.

37. In how many classes is the number of childern less than 500?

(a) 2
(b) 4
(c) 5
(d) 6.

38. In how many classes is the number of childern more than 100?

(a) 6
(b) 4
(c) 3
(d) 1.

39. The ratio of the number of childern of class 6 and 11 is

(a) 3 : 1
(b) 2:1
(c) 2 : 3
(d) 1 : 4.

40. The total number of childern is

(a) 1775
(b) 1675
(c) 1575
(d) 1785.

ANSWERS

HINTS / SOLUTIONS

1. Sunday → 160.
2. Friday → 60.
3. 60 → Friday.
4. 65 – 60 = 5.
5. 160 + 60 = 220.
6. 160 – 60 = 100.
7. Mean = \(\frac { 35+30+45+65+39+20 }{ 6 } \)
= \(\frac { 234 }{ 6 } \) = 39
8. Mean = \(\frac { 10+20+30+40 }{ 4 } \) = \(\frac { 100 }{ 4 } \) = 25.
9. Range = 60 – 45 = 15.
10. Range = 99 – 6 = 93.
11. On each day,rainfall < 6 mm.
12. 4 occurs maximum number (3) times.
13. 32 occurs maximum number (4) times.
14. 1. 2. 3. 4. 5. 6. 7.
15. 10. 15. 20. 25. 30. 35. 40.
17. A coin has two faces.
18. A coin has two faces.
19. A die has six faces.
20. A die has six faces.
21. Apala → 600.
22. Meenu → 100.
23. 600 – 100 = 500.
24. 200 : 400 = 1 : 2.
25. 200, 300, 400, 500 → 4.
26. 400 → Vimla.
27. 400 – 200 = 200; 200 – 100 = 100; 200 = 2 x 100.
28. 100, 200, 300, 400 → 4.
29. 2008 → 500 – 500 = 0.
30. 400 – 200 = 200.
31. 200 : 100 = 2 : 1.
32. 500 – 200 = 300.
33. 250 – 200 = 50.
34. 6 → 400.
35. 11 → 200.
36. 400 – 200 = 200.
37. In each class, number of students < 500.
38. In each class, number of students > 100.
39. 400 : 200 = 2 : 1.
40. 400 + 350 + 320 + 280 + 225 + 200 = 1775.

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