Class 7 Maths Notes for Data Handling

NOTES

CLASS 7
MATHS

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DATA HANDLING
2. I. Important Concepts / Results
3. In our day to day life, we come across many statements that involve the term ―
Average‖. Average is a number indicating the representative of central value of a group
of observations or data. This representative value or central value is known as Measure
of Central Tendency.
4. a) Range = Maximum value of given data - Minimum value of given data
5. a) Arithmetic Mean or Average or Mean = Sum of all observations / Total number of
observations
6. b) Mode : The mode of a set observations is the observation that occurs most often
7. c) Median : The middle most observation of the data arranged in ascending or
descending order
8. d) Graphical representation of data : Bar graph and double bar graph

Examples
i) MCQ
1) The Marks of 11 students of a class are as given below : 78, 11, 99, 63, 94, 6, 78, 36,
30, 55, 22 is
a) 90 b) 91 c) 92 d) 93
Ans :- d) 93
2) The median of the data 20, 30, 40, 10, 15, 25, 35 is
a) 20 b) 25 c) 30 d) 40
Ans: - b) 25
3) The mode of the data 13, 16, 12, 14, 19, 12, 14, 13, 14 is
a) 12 b) 13 c) 14 d) 16
Ans: - c) 14
4) The mean of first five natural number is
a) 4 b) 3 c) 0 d) 2
Ans: - b) 3

ii) Case Study Based Questions:-
Mode of Transport
A survey was conducted for the students studying in class VII of Zedland New school
for the different modes of transport available for them to travel. Sanju and Manju started
from their house to go to school .They had four different options of Mode of transport
available for them to travel

Mode of Transport Distance Covered Time Taken
(in Km) (in hours)
Walking 40 10
Cycle 100 20

25

Car 600 10
Bus 500 25
Read the table and answer the questions:
a) Find the Speed of the bus in Km/h is
Ans: Speed of the bus is Distance / Time = 500 / 25 = 20 km/hr
b) What is the ratio of speed of the car and the cycle?
Ans: Speed of the car is 600/ 10 = 60 km/hr
Speed of the cycle is 100/20 = 5 km /hr
Required Ratio is 60 / 5 = 12:1
c) In the above given information, which mode of the transport has the fastest speed?
Ans: - Car

Short Answer type Questions:-

1) A cricketer scores the following runs in eight innings : 58, 76, 40, 35, 46, 45, 0, 100.
Find the mean score.
Sum of all observations 58+76+40+35+46+45+0+100 400
Solution: Mean Score = Total number of observations = = 8 =
8
50.
2) Find the mode of 7, 6, 5, 3, 0, 3, 4, 8, 2, 4, 5, 2, 4
Solution :Arranging the same numbers together, we get 0, 2,2, 3, 3, 4, 4, 4, 5, 5, 6, 7, 8
Mode is 4 because it occurs most frequently than other observations.
3) Find the median of the data: 24, 36, 46, 17, 18, 25, 35
Solution: We arrange the data in ascending order, we get 17, 18, 24, 25, 35, 36, 46
Median is the middle observation. Therefore 25 is the median.
Long Answer type Questions

1) Following data gives total marks (out of 600) obtained by six children of a particular
class.
Students Ajay Bali Dipti Faiyaz Geetika Hari

Marks 450 500 300 360 40 540
Represent the data on a bar graph.

Solution:

2) A mathematics teacher wants to see,
whether the new technique of teaching she
applied after quarterly test was effective or
not. She takes the scores of the 5 weakest
children in the quarterly test (out of 25) and

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in the half yearly test (out of 25): Draw
double bar for the following data
Solution:

III. Questions for Practice
i) MCQ

1. A batsman scored the following number of runs in six innings: 35, 30, 45, 65, 39 and 20 .The
mean runs scored by him in an inning is
a) 39 b) 38 c) 37 d) 40
2. The marks of 11 students of a class are as given below:
78,11,99,63,94, 6, 78, 36, 30, 55, 22
3. The range of marks is
4. a) 90 b) 91 c) 92 d) 93
5. 3. The mode of the distribution 3, 5, 7, 4, 2, 1, 4, 3, 4 is
6. a) 7 b) 4 c)3 d) 1
7.
8. 4. The median of the distribution 2, 3, 4, 7, 5, 1, 6 is
9. a) 1 b) 2 c) 3 d) 4
10. Number of children in six different classes are given below

Class Number of children

6 400

7 350

8 320

9 280

10 225

11 200

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11. Answer the following related questions ( 5 to 11)
12. 5. In which class is the number of Children maximum?
13. a) 6 b) 7 c) 8 d) 9
14. 6. In which class is the number of children minimum?
15. a) 8 b) 9 c) 10 d)11
16. 7. The difference between the maximum and minimum number of children is
17. a) 100 b ) 200 c) 300 d) 400
18. 8. In how many classes is the number of children less than 500?
19. a) 2 b) 4 c) 5 d) 6
20. 9. In how many classes is the number of children more than 100?
21. a) 6 b) 4 c) 3 d) 1
22. 10. The ratio of the number of children of class 6 and 11 is
23. a) 3:1 b) 2:1 c) 2:3 d)1:4
24. 11. The total number of children is
25. a) 1775 b) 1675 d) 1575 d) 1785
26. ii) Short Answer Type Questions:-
27. 1. The scores in mathematics test (out of 25) of 15 students is as follows:
28. 19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20
29. Find the mode and median of this data. Are they same?
30. 2. The weights (in kg.) of 15 students of a class are:
31. 38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47
32. (i) Find the mode and median of this data. (ii) Is there more than one mode?
33. 3. Find the mode and median of the data: 13, 16, 12, 14, 19, 12, 14, 13, 14
34. 4. Organise the following marks in a class assessment, in a tabular form.
35. 4, 6, 7, 5, 3, 5, 4, 5, 2, 6, 2, 5, 1, 9, 6, 5, 8, 4, 6, 7
36. (i) Which number is the highest? (ii) Which number is the lowest?
37. (iii) What is the range of the data? (iv) Find the arithmetic mean.
38. 5. Find the mean of the first five whole numbers.
39. 6. A cricketer scores the following runs in eight innings:
40. 58, 76, 40, 35, 46, 45, 0, 100.
41. Find the mean score.
42. 7. The enrolment in a school during six consecutive years was as follows:
43. 1555, 1670, 1750, 2013, 2540, 2820
44. Find the mean enrolment of the school for this period.
45. 8. The heights of 10 boys were measured in cm and the results are as follows:
46. 142, 158, 135, 140, 154, 142, 147, 149, 142, 140.
47. Find the median and mode of the above data
48. 9. A cricketer scores the following runs in eight innings: 85, 67, 40, 53, 64, 45, 0, 100.
Find the median score.
49. 10. Heights (in cm) of 25 children are given below:
50. 168, 165, 163, 160, 163, 161, 162, 164, 163, 162, 164, 163, 160, 163, 160, 165, 163, 162,
163, 164, 163, 160, 165, 163, 162

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51. What is the mode of their heights? What do we understand by mode here?
52. Long Answer type Questions:-
53. 1. The rainfall (in mm) in a city on 7 days of a certain week was recorded as follows:

Day Mon Tue Wed Thurs Fri Sat Sun
Rain fall (in 0.0 12.2 2.1 0.0 20.5 5.5 1.0
mm)
54. (i) Find the range of the rainfall in the above data. (ii) Find the mean rainfall for the
week.
55. (iii) On how many days was the rainfall less than the mean rainfall.
56. 2. Consider this data collected from a survey of a colony.

57. (i) Draw a double bar graph choosing an appropriate scale. What do you infer from the
bar graph?
58. (ii) Which sport is most popular?
59. (iii) Which is more preferred, watching or participating in sports?
60. 3. 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:
61. (i) In which subject, has the child improved his performance the most?
62. (ii) In which subject is the improvement the least?
63. (iii) Has the performance gone down in any subject?

64. 4. Number of children in six different classes are given below. Represent the data on a
bar graph.

65. (a) How would you choose a scale?
66. (b) Answer the following questions:
67. (i) Which class has the maximum number of children? And the minimum?
68. (ii) Find the ratio of students of class sixth to the students of class eight.
69. 5. The heights of 10 girls were measured in cm and the results are as follows
70. 135, 150, 139, 128, 151, 132, 146, 149, 143, 141
71. i) What is the height of the tallest girl?
72. ii) What is the height of the shortest girl?

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73. iii) What is the Range of the data?
74. iv) Find the mean of the data?
75. 6. Find the mean, median and mode of the following data :
76. 85, 76, 90, 85, 39, 48, 56, 95, 81, 75
77. Case Study Based Questions:-

78. 1. HIGH SCHOOL
79. Given below is a bar graph representing the
80. percentage of marks obtained by five students
81. in a test studying in high school.
82. Scale :I unit =10% of mark

Answer the following questions based on the graph.

a) What is the average percentage of marks obtained by the 5 pupils in the test?
b) Name the pupil whose marks are 3/4 ofPrateek‘s Marks?

c) Who got minimum marks?
d) What is the Range of Marks of 5 students?
2. GENDER DISTRIBUTION
Study the given graph showing the gender distribution in a few colleges in Zedland .Answer the
questions given below according to the graph :

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a) The total number of girls in colleges D and E together are approximately what percent of the
total number of girls in colleges A, B and C together?

b) What is the respective ratio of the number of boys in college D to the number of boys in
college B?
c) What is the ratio of total number of boys in all the colleges to that of total number of girls?
d) Among the college which college has the best gender equality?
Answers for Questions for Practice
MCQ
1 a 6 d 11 a
2 d 7 b
3 b 8 d
4 d 9 a
5 a 10 b
Short Answers
1 Mode = median = 20, yes they are same
2 Median = 40 kg, Mode = 38 kg and 43 kg
Yes, there are 2 modes ( more than one mode)

3 Median = 14 and Mode = 14

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4
1 1
2 2
3 1
4 3
5 5
6 4
7 2
8 1
9 1

i) 9 ii) 1 iii) 8 iv) 5
5 3
6 50
7 2058
8 Median = Mode = 142
9 58.5
10 14
Long Answers
1. i) 20.5 m ii) 5.9 m iii) 5 days ( Mon, Wed, Thu, Sat and Sun)
2.

3.

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4.

5.i) 151cm ii)128cm, iii) 23cm iv) 141.4 cm v) 5 ( 143, 146, 149, 150, 151)
6. mean = 73, Median = 78.5 and Mode = 85
Case Study Based Questions
1) a) 72 b) Rohit c) Mohit d) 50
2) a) 87% b) 4:5 c) 59: 70 d) A
Chapter Test
Class 7 Marks : 20
I Choose the correct answer:- 2 x 1 =2 marks
1. A batsman scored the following number of runs in six innings: 35, 30, 45, 65, 39 and
20 . The mean runs scored by him in an inning is
a) 39 b) 38 c) 37 d) 40
2. The median of the distribution 2, 3, 4, 7, 5, 1, 6 is
a) 1 b) 2 c) 3 d) 4
II. Answer the following : 3 X 2 = 6 Marks
3. The heights of 10 boys were measured in cm and the results are as follows:
142, 158, 135, 140, 154, 142, 147, 149, 142, 140.
Find the median and mode of the above data
4. Find the mean of the first five whole numbers.
5. A cricketer scores the following runs in eight innings:
58, 76, 40, 35, 46, 45, 0, 100. Find the mean score.
III. Answer the following:- 3 x 4 = 12 Marks
6. 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:

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(i) In which subject, has the child improved his performance the most?
(ii) In which subject is the improvement the least?
7. Number of children in six different classes are given below. Represent the data on a bar graph.

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.
8. 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) Find the mean of the data?
Chapter Test
Data Handling
Marks : 30
I Choose the correct answer:- 4 x 1 =4 marks
1) The Marks of 11 students of a class are as given below : 78, 11, 99, 63, 94, 6, 78, 36, 30,
55, 22 is
a) 90 b) 91 c) 92 d) 93
2) The median of the data 20, 30, 40, 10, 15, 25, 35 is
a) 20 b) 25 c) 30 d) 40
3) The mode of the data 13, 16, 12, 14, 19, 12, 14, 13, 14 is
a) 12 b) 13 c) 14 d) 16
4) The mean of first five natural number is
a) 4 b) 3 c) 0 d) 2
II. Answer the following : 3 × 2 = 6 Marks
5. Find the mean of first five prime numbers,
6. Find the mode of 7, 6, 5, 3, 0, 3, 4, 8, 2, 4, 5, 2, 4
7. Find the median of the data: 24, 36, 46, 17, 18, 25, 35
III. Answer the following:-3× 4 = 12Marks
8. The rainfall (in mm) in a city on 7 days of a certain week was recorded as follows:
Day Mon Tue Wed Thurs Fri Sat Sun
Rain fall (in 0.0 12.2 2.1 0.0 20.5 5.5 1.0
mm)
(i) Find the range of the rainfall in the above data. (ii) Find the mean rainfall for the week.

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(iii) On how many days was the rainfall less than the mean rainfall.
9. . Consider this data collected from a survey of a colony.

(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?
10. 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.
Case Study Based Questions :- 2 × 4 = 8 marks
11. GENDER DISTRIBUTION
Study the given graph showing the gender distribution in a few colleges in Zedland .Answer
the questions given below according to the graph :

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a) The total number of girls in colleges D and E together are approximately what percent of
the total number of girls in colleges A, B and C together?

b) What is the respective ratio of the number of boys in college D to the number of boys in
college B?
c) What is the ratio of total number of boys in all the colleges to that of total number of
girls?
d) Among the college which college has the best gender equality?
12. HIGH SCHOOL
Given below is a bar graph representing the percentage of marks obtained by five students in
a test studying in high school.
Scale :I unit =10% of marks

Answer the following questions based on the graph.
a) What is the average percentage of marks obtained by the 5 pupils in the test?
b) Name the pupil whose marks are 3/4 ofPrateek‘s Marks?
c) Who got minimum marks?
d) What is the Range of Marks of 5 students?

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Study Materials
Notes

Model Papers Class 6 Notes

Sample Papers Class 7 Notes
Half Yearly Sample Papers Class 8 Notes

Class 9 Notes
Important Resources
Class 10 Notes
Periodic Table
Class 11 Notes
Writing Skills / Formats

Maps of India / World Class 12 Notes

Books and Solutions

NCERT Books
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HC Verma Chapter Wise Solutions
RD Sharma Solutions
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