Selina Solutions Concise Maths Class 10 Chapter 23 Graphical Representation (Histograms and Ogives)

A statistical data can be expressed by diagram, chart, etc., in order to make the data grasped immediately. In this chapter, students will be studying only about histograms, frequency polygon and Ogive (cumulative frequency curve). This chapter consists of only one exercise, solutions which can be found at Selina Solutions for Class 10 Mathematics. This is a vital resource for students in order to prepare for their exams. It is prepared by experienced faculty at BYJU’S, keeping in mind the latest ICSE guidelines. Additionally, this resource is available free of cost and can be accessed at any time. Further, the Selina Solutions for Class 10 Mathematics Chapter 23 Graphical Representation (Histograms and Ogives) are available in a PDF, provided in the link below.

Selina Solutions Concise Maths Class 10 Chapter 23 Graphical Representation (Histograms and Ogives) Download PDF

 

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Access Selina Solutions Concise Maths Class 10 Chapter 23 Graphical Representation (Histograms and Ogives)

Exercise 23 Page No: 348

1. Draw histograms for the following frequency distributions:

(i)

Class Interval

0-10

10-20

20-30

30-40

40-50

50-60

Frequency

12

20

26

18

10

6

(ii)

Class Interval

10-16

16-22

22-28

28-34

34-40

Frequency

15

23

30

20

16

(iii)

Class Interval

30-39

40-49

50-59

60-69

70-79

Frequency

24

16

09

15

20

(iv)

Class Marks

16

24

32

40

48

56

64

Frequency

8

12

15

18

25

19

10

Solution:

(i)

Class Interval

Frequency

0-10

12

10-20

20

20-30

26

30-40

18

40-50

10

50-60

06

Selina Solutions Concise Class 10 Maths Chapter 23 ex. 23 - 1

Steps of construction:

(a) Taking suitable scales, mark the class intervals on x-axis and the frequencies 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

Selina Solutions Concise Class 10 Maths Chapter 23 ex. 23 - 2

Steps of construction:

(a) Taking suitable scales, mark the 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

Selina Solutions Concise Class 10 Maths Chapter 23 ex. 23 - 3

Steps of construction:

(a) Convert the data into exclusive form. [Here, adjustment factor = 0.5]

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

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

(iv)

From the given data:

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

Selina Solutions Concise Class 10 Maths Chapter 23 ex. 23 - 4

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.

2. Draw cumulative frequency curve (ogive) for each of the following distributions:

(i)

Class

Interval

10-15

15-20

20-25

25-30

30-45

35-40

Frequency

10

15

17

12

10

08

(ii)

Class Interval

10-19

20-29

30-39

40-49

50-59

Frequency

23

16

15

20

12

Solution:

(i)

Class Interval

Frequency

10-15

10

15-20

15

20-25

17

25-30

12

30-35

10

35-40

08

Selina Solutions Concise Class 10 Maths Chapter 23 ex. 23 - 5

Steps of construction:

(a) Taking suitable scales, mark the class intervals on x-axis and the frequencies 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

Selina Solutions Concise Class 10 Maths Chapter 23 ex. 23 - 6

Steps of construction:

(a) Convert the data into exclusive form. [Here, adjustment factor = 0.5]

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

3. Draw an ogive for each of the following distributions:

(i)

Marks Obtained

less

than 10

less

than 20

less

than30

less

than 40

less

than 50

No. of

Students

8

25

38

50

67

(ii)

Age in years (less than)

10

20

30

40

50

60

70

Cumulative Frequency

0

17

32

37

53

58

65

Solution:

(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

Selina Solutions Concise Class 10 Maths Chapter 23 ex. 23 - 7

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

Selina Solutions Concise Class 10 Maths Chapter 23 ex. 23 - 8

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.

4. Construct a frequency distribution table for the number given below, using the class intervals 21-30, 31-40 … etc.

75, 67, 57, 50, 26, 33, 44, 58, 67, 75, 78, 43, 41, 31, 21, 32, 40, 62, 54, 69, 48, 47, 51, 38, 39, 43, 61, 63, 68, 53, 56, 49, 59, 37, 40, 68, 23, 28, 36, 47

Use the table obtained to draw:

(i) a histogram (ii) an ogive

Solution:

Selina Solutions Concise Class 10 Maths Chapter 23 ex. 23 - 9

(i)

Selina Solutions Concise Class 10 Maths Chapter 23 ex. 23 - 10

(ii)

Selina Solutions Concise Class 10 Maths Chapter 23 ex. 23 - 11

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.

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