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Selina Concise Mathematics - Part II Solution for Class 10 Mathematics Chapter 23 - Graphical Representation (Histograms and Ogives)

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Selina Textbook Solutions Chapter 23 - Graphical Representation (Histograms and Ogives)

Selina Textbook Solutions are a perfect way to ace your examination with high marks. These Textbook Solutions are extremely helpful for solving difficult questions in the ICSE Class 10 Mathematics exam. Our Selina Textbook Solutions are written by our subject experts. Find all the answers to the Selina textbook questions of Chapter 23 - Graphical Representation (Histograms and Ogives).

All Selina textbook questions of Chapter 23 - Graphical Representation (Histograms and Ogives) solutions are created in accordance with the latest ICSE syllabus. These free Textbook Solutions for ICSE Class 10 Selina Concise Mathematics will give you a deeper insight on the fundamentals in this chapter and will help you to score more marks in the final examination. ICSE Class 10 students can refer to these solutions while doing their homework and while studying and revising for the Mathematics exam. 

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Selina Concise Mathematics - Part II Solution for Class 10 Mathematics Chapter 23 - Graphical Representation (Histograms and Ogives) Page/Excercise 23

Solution 1

(i)

Class Interval

Frequency

0-10

12

10-20

20

20-30

26

30-40

18

40-50

10

50-60

06

Steps of construction:

(a) Taking suitable scales, mark class intervals on x-axis and frequency on y-axis.

(b)Construct rectangles with class intervals as bases and corresponding frequencies as heights.

(ii)

Class Interval

Frequency

10-16

15

16-22

23

22-28

30

28-34

20

34-40

16

Steps of construction:

(a) Taking suitable scales, mark class intervals on x-axis and frequency on y-axis.

(b) Construct rectangles with class intervals as bases and corresponding frequencies as heights.

(iii)

Class Interval

(Inclusive form)

Class Interval

(Exclusive Form)

Frequency

30-39

29.5-39.5

24

40-49

39.5-49.5

16

50-59

49.5-59.5

09

60-69

59.5-69.5

15

70-79

69.5-79.5

20

Steps of construction:

(a) Convert the data into exclusive form.

(b) Taking suitable scales, mark class intervals on x-axis and frequency on y-axis.

(c) Construct rectangles with class intervals as bases and corresponding frequencies as heights.

(iv)

Class Marks

Class Intervals

Frequency

16

12-20

08

24

20-28

12

32

28-36

15

40

36-44

18

48

44-52

25

56

52-60

19

64

60-68

10

Steps of construction:

(a) Convert the class marks into class intervals.

(b) Taking suitable scales, mark class intervals on x-axis and frequency on y-axis.

(c) Construct rectangles with class intervals as bases and corresponding frequencies as heights.

Solution 2

(i)

Class Interval

Frequency

10-15

10

15-20

15

20-25

17

25-30

12

30-35

10

35-40

08

 

Steps of construction:

(a) Taking suitable scales, mark class intervals on x-axis and frequency on y-axis.

(b) Construct rectangles with class intervals as bases and corresponding frequencies as heights.

( c) Join the mid-points of the rectangle to obtain the ogive.

(ii)

Class Interval

(Inclusive)

Class Interval

(Exclusive)

Frequency

Cumulative

Frequency

10-19

9.5-19.5

23

23

20-29

19.5-29.5

16

39

30-39

29.5-39.5

15

54

40-49

39.5-49.5

20

74

50-59

49.5-59.5

12

86

   

Total

86

 

Steps of construction:

(a) Convert the data into exclusive form.

(b) Taking suitable scales, mark class intervals on x-axis and frequency on y-axis.

(c) Construct rectangles with class intervals as bases and corresponding frequencies as heights.

(d) Join the mid-points of the rectangle to obtain the ogive.

Solution 3

(i)

Marks Obtained

No. of students (c.f.)

less than 10

8

less than 20

25

less than 30

38

less than 40

50

less than 50

67

 

Steps Of construction:

(a) Plot the points (10,8), (20, 25), (30, 38), (40, 50) and (50, 67) on the graph.

(b) Join them with free hand to obtain an ogive.

(ii)

Age in years

(less than)

Cumulative

Frequency

10

0

20

17

30

32

40

37

50

53

60

58

70

65

 

 

Steps Of construction:

(a) Plot the points (10, 0), (20, 17), (30, 32), (40, 37), (50, 53), (60, 58) and (70, 65) on the graph.

(b) Join them with free hand to obtain an ogive.

Solution 4


(i)

(ii)

Plot the points (30,4), (40,13), (50,22), (60,29), (70,37) and (80,40) on the graph and join them with free hand to obtain an ogive.

Solution 5

(a)

Class Interval

Frequency

c.f.

8-12

9

9

12-16

16

25

16-20

22

47

20-24

18

65

24-28

12

77

28-32

4

81

(b) Now plot the points (12, 9), (16, 25), (20, 47), (24, 65), (28, 77), (32, 81) and join them to obtain an ogive.

Solution 6

(a)

Difference in consecutive class marks = 17.5 - 12.5 = 5

first class interval will be 10-15 and so on.

Class Mark

Class Interval

Frequency

c.f.

12.5

10-15

12

12

17.5

15-20

17

29

22.5

20-25

22

51

27.5

25-30

27

78

32.5

30-35

30

108

37.5

35-40

21

129

42.5

40-45

16

145

Total = 145

(b)

Now plot the points (15,12), (20,29), (25,51), (30,78), (35,108), (40,129), (45,145) and join them to obtain an ogive.

Solution 7

(i)

 

Wages

No. Of workers

c.f.

6500-7000

10

10

7000-7500

18

28

7500-8000

22

50

8000-8500

25

75

8500-9000

17

92

9000-9500

10

102

9500-10000

8

110

Total = 110

Now plot the points (7000,10), (7500,28), (8000,50), (8500,75), (9000,92), (9500,102) and (10000,110) and join them to obtain an ogive.

Solution 8

Height (in cm)

No. Of workers

c.f.

150-155

6

6

155-160

12

18

160-165

18

36

165-170

20

56

170-175

13

69

175-180

8

77

180-185

6

83

We plot the points (155, 6), (160, 18), (165, 36), (170, 56), (175, 69),

(180, 77) and (185, 83) on the graph and join them in free hand to obtain an ogive.

Solution 9

(i)

Marks

(less than)

Cumulative frequency

Frequency

0-10

7

7

10-20

28

28-7=21

20-30

54

54-28=26

30-40

71

71-54=17

40-50

84

84-71=13

50-60

105

105-84=21

60-70

147

147-105=42

70-80

180

180-147=33

80-90

196

196-180=16

90-100

200

200-196=4

Total

200

(ii)

Marks

(more than)

Cumulative frequency

Frequency

0-10

100

13

10-20

87

22

20-30

65

10

30-40

55

13

40-50

42

6

50-60

36

5

60-70

31

10

70-80

21

3

80-90

18

11

90-100

7

7

Total

100

TopperLearning provides step-by-step solutions for each question in each chapter. Access Chapter 23 - Graphical Representation (Histograms and Ogives)  for ICSE Class 10 Mathematics free of cost. The solutions are provided by our subject matter experts. Refer to our solutions for the Selina Concise Mathematics textbook to revise the whole chapter and clear your fundamentals before the examination. By referring to the solutions for this chapter and the others, we hope that you are able to write your exams well. 

Text Book Solutions

ICSE X - Mathematics

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