Frank Solutions for Class 10 Maths Chapter 23 Graphical Representation

Frank Solutions for Class 10 Maths Chapter 23 Graphical Representation, are provided here. Our solution module employs numerous shortcut tips and practical examples to explain all the exercise questions in a simple and easily understandable language. Our expert tutors at BYJU’S have simplified the difficult problems into simple steps, which can be easily solved by students at ease. These solutions will help you in obtaining knowledge and strong command over the subject. Download pdf of Frank Solutions for Class 10 Maths Chapter 23 in their respective links.

Chapter 23 – Graphical Representation, a graph is defined as a pictorial representation or a diagram that represents data or values in an organised manner. As the chapter is about Graphs, here we learn how to plot the graph, draw the histogram graph and read the details from the graph and further solve the same.

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Access answers to Frank Solutions for Class 10 Maths Chapter 23 Graphical Representation

1. Construct histograms for each of the following frequency distributions:

(i)

Class Interval

0 – 10

10 – 20

20 – 30

30 – 40

40 – 50

50 – 60

Frequency

8

20

34

22

10

6

Solution:-

Steps to construct histograms for given frequency distributions,

1. On the x – axis, take 1 cm = 5 units and plot class interval.

2. On the y – axis, take 1 cm = 5 units and plot frequency.

3. Draw rectangles of histograms as per the given frequency distribution.

Frank Solutions for Class 10 Maths Chapter 23 Image 1

(ii)

Class Interval

130 – 140

140 – 150

150 – 160

160 – 170

170 – 180

Frequency

24

16

29

20

11

Solution:-

Steps to construct histograms for given frequency distributions,

1. On the x – axis, take 1 cm = 5 units and plot class interval.

2. On the y – axis, take 1 cm = 5 units and plot frequency.

3. Draw rectangles of histograms as per the given frequency distribution.

Frank Solutions for Class 10 Maths Chapter 23 Image 2

(iii)

Class Interval

1 – 10

11 – 20

21 – 30

31 – 40

41 – 50

Frequency

11

23

30

20

16

Solution:-

Steps to construct histograms for given frequency distributions,

1. First we have to make the class intervals continuous by subtracting 0.5 from the lower limit of each class and add 0.5 to the upper limit of each class.

Then we have,

Class Interval

0.5 – 10.5

10.5 – 20.5

20.5 – 30.5

30.5 – 40.5

40.5 – 50.5

Frequency

11

23

30

20

16

2. On the x – axis, take 1 cm = 5 units and plot class interval.

3. On the y – axis, take 1 cm = 5 units and plot frequency.

4. Draw rectangles of histograms as per the obtained data.

Frank Solutions for Class 10 Maths Chapter 23 Image 3

(iv)

Class Interval

110 – 119

120 – 129

130 – 139

140 – 149

150 – 159

Frequency

15

23

30

20

16

Solution:-

Steps to construct histograms for given frequency distributions,

1. First we have to make the class intervals continuous by subtracting 0.5 from the lower limit of each class and add 0.5 to the upper limit of each class.

Then we have,

Class Interval

109.5 – 119.5

119.5 – 129.5

129.5 – 139.5

139.5 – 149.5

149.5 – 159.5

Frequency

15

23

30

20

16

2. On the x – axis, take 1 cm = 5 units and plot class interval.

3. On the y – axis, take 1 cm = 5 units and plot frequency.

4. Draw rectangles of histograms as per the obtained data.

Frank Solutions for Class 10 Maths Chapter 23 Image 4

(vi)

Class Mark

6

12

18

24

30

36

Frequency

8

12

15

18

25

7

Solution:-

Steps to construct histograms for given frequency distributions,

1. First we have to calculate the class interval from the class mark using the following adjustment formula.

Value of Adjustment = (One class mark – Preceding class mark)/2

Then, the value obtained is added to the class mark to obtain the upper limit and subtracted from the class mark to obtain lower limit.

Now,

Value of adjustment = (12 – 6)/2

= 6/2

= 3

So, we add and subtract 3 to each class mark to obtain the class interval.

The lower limit of first class = 6 – 3 = 3

The Upper limit of first class = 6 + 3 = 9

Hence, the first class interval is (3 – 9).

Similarly, we can calculate the remaining class intervals.

Class Mark

3 – 9

9 -15

15 – 21

21 – 27

27 – 33

33 – 39

Frequency

8

12

15

18

25

7

2. On the x – axis, take 1 cm = 5 units and plot class interval.

3. On the y – axis, take 1 cm = 5 units and plot frequency.

4. Draw rectangles of histograms as per the obtained data.

Frank Solutions for Class 10 Maths Chapter 23 Image 5

2. Construct a histogram and then a frequency polygon for each of the following frequency distribution:

(i)

Class Interval

0 – 10

10 – 20

20 – 30

30 – 40

40 – 50

50 – 60

Frequency

8

13

27

35

14

3

Solution:-

Steps to construct histograms for given frequency distributions,

1. On the x – axis, take 1 cm = 5 units and plot class interval.

2. On the y – axis, take 1 cm = 5 units and plot frequency.

3. Draw rectangles of histograms as per the given frequency distribution.

4. Then, for each rectangle mark the midpoint of its length at the top.

5. So, in the graph midpoints are (5, 8), (15, 13), (25, 27), (35, 35), (45, 14), (55, 3)

6. Also mark two more midpoints of zero frequency on x – axis at the start and at the end.

7. Finally Connect the points using straight lines.

Frank Solutions for Class 10 Maths Chapter 23 Image 6

(ii)

Class Interval

11 – 20

21 – 30

31 – 40

41 – 50

51 – 60

61 – 70

Frequency

15

28

50

35

20

12

Solution:-

Steps to construct histograms for given frequency distributions,

1. First we have to make the class intervals continuous by subtracting 0.5 from the lower limit of each class and add 0.5 to the upper limit of each class.

Then we have,

Class Interval

10.5 – 20.5

20.5 – 30.5

30.5 – 40.5

40.5 – 50.5

50.5 – 60.5

60.5 – 70.5

Frequency

15

28

50

35

20

12

2. On the x – axis, take 1 cm = 5 units and plot class interval.

3. On the y – axis, take 1 cm = 5 units and plot frequency.

4. Draw rectangles of histograms as per the given frequency distribution.

5. Then, for each rectangle mark the midpoint of its length at the top.

6. So, in the graph midpoints are (15.5, 15), (25.5, 28), (35.5, 50), (45.5, 35), (55.5, 20), (65.5, 12)

7. Also mark two more midpoints of zero frequency on x – axis at the start and at the end.

8. Finally Connect the points using straight lines.

Frank Solutions for Class 10 Maths Chapter 23 Image 7

(iii)

Class Interval

100 – 150

150 – 200

200 – 250

250 – 300

300 – 350

Frequency

10

15

17

12

10

Solution:-

Steps to construct histograms for given frequency distributions,

1. On the x – axis, take 1 cm = 5 units and plot class interval.

2. On the y – axis, take 1 cm = 5 units and plot frequency.

3. Draw rectangles of histograms as per the given frequency distribution.

4. Then, for each rectangle mark the midpoint of its length at the top.

5. So, in the graph midpoints are (125, 10), (175, 15), (225, 17), (275, 12), (325, 10).

6. Also mark two more midpoints of zero frequency on x – axis at the start and at the end.

7. Finally Connect the points using straight lines.

Frank Solutions for Class 10 Maths Chapter 23 Image 8

3. Construct a frequency polygon without using a histogram for the following frequency distribution:

(i)

Class Mark

10

15

20

25

30

35

40

Frequency

4

20

40

45

30

25

5

Solution:-

Steps to construct histograms for given frequency distributions,

1. On the x – axis, take 1 cm = 5 units and plot class interval.

2. On the y – axis, take 1 cm = 5 units and plot frequency.

3. So, in the graph mark the given data.

4. Also mark two more midpoints of zero frequency on x – axis at the start and at the end.

5. Finally Connect the points using straight lines.

Frank Solutions for Class 10 Maths Chapter 23 Image 9

(ii)

Class Interval

10 – 20

20 – 40

40 – 60

60 – 80

80 – 100

Frequency

9

17

15

20

14

Solution:-

Steps to construct histograms for given frequency distributions,

1. On the x – axis, take 1 cm = 5 units and plot class interval.

2. On the y – axis, take 1 cm = 5 units and plot frequency.

Class Interval

Class mark

Frequency

10 – 20

(10 + 20)/2 = 15

9

20 – 40

(20 + 40)/2 = 30

17

40 – 60

(40 + 60)/2 = 50

15

60 – 80

(60 + 80)/2 = 70

20

80 – 100

(80 + 100)/2 = 90

14

3. So, in the graph mark the points (15, 9), (30, 17), (50, 15), (70, 20), (90, 14).

4. Also mark two more midpoints of zero frequency on x – axis at the start and at the end.

5. Finally Connect the points using straight lines
Frank Solutions for Class 10 Maths Chapter 23 Image 10

(iii)

Class Interval

1 – 10

11 – 20

21 – 30

31 – 40

41 – 50

Frequency

8

12

10

16

6

Solution:-

Steps to construct histograms for given frequency distributions,

1. First we have to make the class intervals continuous by subtracting 0.5 from the lower limit of each class and add 0.5 to the upper limit of each class.

Then we have,

Class Interval

0.5 – 10.5

10.5 – 20.5

20.5 – 30.5

30.5 – 40.5

40.5 – 50.5

Frequency

8

12

10

16

6

2. On the x – axis, take 1 cm = 5 units and plot class interval.

3. On the y – axis, take 1 cm = 5 units and plot frequency.

Then,

Class Interval

Class mark

Frequency

0.5 – 10.5

(0.5 + 10.5)/2 = 5.5

8

10.5 – 20.5

(10.5 + 20.5)/2 = 15.5

12

20.5 – 30.5

(20.5 + 30.5)/2 = 25.5

10

30.5 – 40.5

(30.5 + 40.5)/2 = 35.5

16

40.5 – 50.5

(40.5 + 50.5)/2 = 45.5

6

3. So, in the graph mark the points (5.5, 8), (15.5, 12), (25.5, 10), (35.5, 16), (45.5, 6).

4. Also mark two more midpoints of zero frequency on x – axis at the start and at the end.

5. Finally Connect the points using straight lines.

Frank Solutions for Class 10 Maths Chapter 23 Image 11

4. Draw an ogive for the following:

(i)

Class Interval

0 – 10

10 – 20

20 – 30

30 – 40

40 – 50

Frequency

8

12

10

14

6

Solution:-

Steps to construct histograms for given frequency distributions,

1. On the x – axis, take 1 cm = 5 units and plot class interval.

2. On the y – axis, take 1 cm = 5 units and plot frequency.

Then,

Less than

Cumulative Frequency

10

8

20

20

30

30

40

44

50

50

3. So, in the graph mark the points with coordinates having abscissae as actual limits and ordinates as the cumulative frequencies, (10, 8), (20, 20), (30, 30), (40, 44), (50, 50).

4. Finally join the points plotted by a smooth curve.

Frank Solutions for Class 10 Maths Chapter 23 Image 12

(ii)

Class Interval

100 – 150

150 – 200

200 – 250

250 – 300

300 – 350

350 – 400

Frequency

10

13

17

12

10

8

Solution:-

Steps to construct histograms for given frequency distributions,

1. On the x – axis, take 1 cm = 5 units and plot class interval.

2. On the y – axis, take 1 cm = 5 units and plot frequency.

Then,

Less than

Cumulative Frequency

150

10

200

23

250

40

300

52

350

62

400

70

3. So, in the graph mark the points with coordinates having abscissae as actual limits and ordinates as the cumulative frequencies, (150, 10), (200, 23), (250, 40), (300, 52), (350, 62), (400, 70).

4. Finally join the points plotted by a smooth curve.

Frank Solutions for Class 10 Maths Chapter 23 Image 13

(iii)

Class Interval

10 – 19

20 – 29

30 – 39

40 – 49

50 – 59

Frequency

28

23

15

20

14

Solution:-

Steps to construct histograms for given frequency distributions,

1. On the x – axis, take 1 cm = 5 units and plot class interval.

2. On the y – axis, take 1 cm = 5 units and plot frequency.

Then,

Less than

Cumulative Frequency

19

28

29

51

39

66

49

86

59

100

3. So, in the graph mark the points with coordinates having abscissae as actual limits and ordinates as the cumulative frequencies, (19, 28), (29, 51), (39, 66), (49, 86), (59, 100).

4. Finally join the points plotted by a smooth curve.

Frank Solutions for Class 10 Maths Chapter 23 Image 14

(iv)

Marks obtained

Less than 10

Less than 20

Less than 30

Less than 40

Less than 50

Number of Students

8

22

48

60

75

Solution:-

Steps to construct histograms for given frequency distributions,

1. On the x – axis, take 1 cm = 5 units and plot class interval.

2. On the y – axis, take 1 cm = 5 units and plot frequency.

Then,

Marks less than

Cumulative Frequency

10

8

20

22

30

48

40

60

50

75

3. So, in the graph mark the points with coordinates having abscissae as actual limits and ordinates as the cumulative frequencies, (10, 8), (20, 22), (30, 48), (40, 60), (50, 75).

4. Finally join the points plotted by a smooth curve.

Frank Solutions for Class 10 Maths Chapter 23 Image 15

(v)

Age in years

Less than 10

Less than 20

Less than 30

Less than 40

Less than 50

Number of people

0

17

42

67

100

Solution:-

Steps to construct histograms for given frequency distributions,

1. On the x – axis, take 1 cm = 5 units and plot class interval.

2. On the y – axis, take 1 cm = 5 units and plot frequency.

Then,

Marks less than

Cumulative Frequency

10

0

20

17

30

42

40

67

50

100

3. So, in the graph mark the points with coordinates having abscissae as actual limits and ordinates as the cumulative frequencies, (10, 0), (20, 17), (30, 42), (40, 67), (50, 100).

4. Finally join the points plotted by a smooth curve.

Frank Solutions for Class 10 Maths Chapter 23 Image 16

(vi)

Marks obtained

More than 10

More than 20

Less than 30

Less than 40

Less than 50

Number of students

8

25

38

50

67

Solution:-

Steps to construct histograms for given frequency distributions,

1. With lower limits of class intervals and from cumulative frequency, subtract the frequency of each class to obtain cumulative frequency distribution.

2. Then mark lower class limits along x – axis, take 1 cm = 5 unit.

3. Also mark cumulative frequency along y – axis, take 1 cm = 5 unit.

Then,

Marks more than

Frequency

Cumulative Frequency

10

8

188

20

25

180

30

38

155

40

50

117

50

67

67

4. So, in the graph mark the points (x, f), where x is the lower limit of one class and f is the corresponding cumulative frequency (10, 188), (20, 180), (30, 155), (40, 117), (50, 67).

5. Finally join the points plotted by a smooth curve.

Frank Solutions for Class 10 Maths Chapter 23 Image 17

(vii)

Marks

(more than)

0

10

20

30

40

50

60

70

80

90

100

Cumulative Frequency

100

87

65

55

42

36

31

21

18

7

0

Solution:-

Solution:-

Steps to construct histograms for given frequency distributions,

1. With lower limits of class intervals and from cumulative frequency, subtract the frequency of each class to obtain cumulative frequency distribution.

2. Then mark lower class limits along x – axis, take 1 cm = 5 unit.

3. Also mark cumulative frequency along y – axis, take 1 cm = 5 unit.

Then,

Marks more than

Cumulative Frequency

0

100

10

87

20

65

30

55

40

42

50

36

60

31

70

21

80

18

90

7

100

0

4. So, in the graph mark the points (x, f), where x is the lower limit of one class and f is the corresponding cumulative frequency, (0, 100), (10, 87), (20, 65), (30, 55), (40, 42), (50, 36), (60, 31), (70, 21), (80, 18), (90, 7), (100, 0).

5. Finally join the points plotted by a smooth curve.

Frank Solutions for Class 10 Maths Chapter 23 Image 18

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