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Class 10 SELINA Solutions Maths Chapter 23 - Graphical Representation (Histograms and Ogives)

Graphical Representation (Histograms and Ogives) Exercise Ex. 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

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