Frank Solutions Class 9 Maths Chapter 23 Graphical Representation of Statistical Data

Frank Solutions Class 9 Maths Chapter 23 Graphical Representation of Statistical Data provides students 100% answers in a lucid manner. Students who have doubts relying on the covered concepts, are advised to follow Frank Solutions and clear their doubts quickly. Practising Frank Solutions on a regular basis enhances their skills, which are essential to boost exam preparation. Students can access Frank Solutions Class 9 Maths Chapter 23 Graphical Representation of Statistical Data PDF, from the links provided below.

Chapter 23 Graphical Representation of Statistical Data has problems which gives information of data using graphs. The way of analyzing numerical data is known as graphical representation. Referring to Frank Solutions helps students to speed up their problem solving skills, which is an important aspect from an exam point of view.

Frank Solutions for Class 9 Maths Chapter 23 Graphical Representation of Statistical Data Download PDF

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Access Frank Solutions for Class 9 Maths Chapter 23 Graphical Representation of Statistical Data

1. Harmeet earns Rs 50,000 per month. He budget for his salary as per the following table:

Expenses

Accommodation

Food

Clothing

Travel

Miscellaneous

Savings

Amount (Rs)

12000

9000

2500

7500

4000

15000

Draw a bar graph for the above data.

Solution:

The bar graph for the above data is as follows:

FRANK Solutions Class 9 Maths Chapter 23 - 1

2. The birth rate per thousand of the following states over a certain period is given below:

States

Punjab

Haryana

U.P.

Gujarat

Rajasthan

Jammu and Kashmir

Birth Rate (per thousand)

22.9

21.8

19.5

21.1

23.9

18.3

Draw a bar graph for the above data

Solution:

The bar graph for the above data is shown below

FRANK Solutions Class 9 Maths Chapter 23 - 2

3. Fadil, a class IX student, scored marks in different subjects (each out of total 100) during his annual examination as given below

Subject

Maths

English

Science

Social Studies

Hindi

Physical Education

Mark (out of 100)

75

80

77

78

67

89

Draw horizontal bar graph for the above data.

Solution:

The horizontal bar graph for the above data is as follows:

FRANK Solutions Class 9 Maths Chapter 23 - 3

4. The number of students in different sections of class IX of a certain school is given in the following table.

Section

IX – A

IX – B

IX – C

IX – D

IX – E

Number of students

48

40

50

45

38

Draw horizontal bar graph for the above data.

Solution:

The horizontal bar graph for the above data is given below

FRANK Solutions Class 9 Maths Chapter 23 - 4

5. The number of students (boys and girls) of class IX participating in different activities during their annual day function is given below:

Activities

Dance

Speech

Singing

Quiz

Drama

Anchoring

Boys

12

5

4

4

10

2

Girls

10

8

6

3

9

1

Draw a double bar graph for the above data.

Solution:

The double bar graph for the above data is shown below

FRANK Solutions Class 9 Maths Chapter 23 - 5

6. Draw a histogram for the following frequency distribution:

Train fare

0 – 50

50 – 100

100 – 150

150 – 200

200 – 250

250 – 300

No. of travellers

25

40

36

20

17

12

Solution:

This is an exclusive frequency distribution. We represent the class limits on the x-axis on a suitable scale and the frequencies on the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, we construct rectangles to obtain a histogram of the given frequency distribution.

The histogram for the above frequency distribution is shown below

FRANK Solutions Class 9 Maths Chapter 23 - 6

7. Draw a histogram for the following frequency table:

Class Interval

5 – 9

10 – 14

15 – 19

20 – 24

25 – 29

30 – 34

Frequency

5

9

12

10

16

12

Solution:

We see that the class intervals are in an inclusive manner. First, we need to convert them into exclusive manner.

Class interval

Frequency

4.5 – 9.5

5

9.5 – 14.5

9

14.5 – 19.5

12

19.5 – 24.5

10

24.5 – 29.5

16

29.5 – 34.5

12

We take the true class limits on the x-axis on a suitable scale and the frequencies on the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, we construct rectangles to obtain a histogram of the given frequency distribution.

Here, as the class limits do not start from 0, we put a kink between 0 and the true lower boundary of the first class.

The histogram for the given frequency table is shown below

FRANK Solutions Class 9 Maths Chapter 23 - 7

8. Draw a histogram for the following cumulative frequency table:

Marks

Less than 10

Less than 20

Less than 30

Less than 40

Less than 50

Less than 60

Number of student

7

18

30

45

55

60

Solution:

Marks

0 – 10

10 – 20

20 – 30

30 – 40

40 – 50

50 – 60

Number of students

7

11

12

15

10

5

The histogram for the cumulative frequency table is shown below

FRANK Solutions Class 9 Maths Chapter 23 - 8

9. Draw a histogram for the following cumulative frequency table:

Class interval

0 – 10

10 – 20

20 – 30

30 – 40

40 – 50

Cumulative Frequency

6

10

18

32

40

Solution:

First convert the cumulative frequency table to an exclusive frequency distribution table.

Class interval

0 – 10

10 – 20

20 – 30

30 – 40

40 – 50

Cumulative Frequency

6

4

8

14

8

We take the class limits on the x-axis and the frequencies on the y-axis on suitable scales. We draw rectangles with the class intervals as bases and the corresponding frequencies as heights. The histogram for the given cumulative frequency table is shown below

FRANK Solutions Class 9 Maths Chapter 23 - 9

10. Draw a histogram and a frequency polygon for the following data:

Marks

0 – 20

20 – 40

40 – 60

60 – 80

80 – 100

Number of students

12

18

30

25

15

Solution:

We represent the class limits on the x-axis and the frequencies on the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, we construct rectangles to obtain a histogram of the given frequency distribution.

Now,

Take the mid-points of the upper horizontal side of each rectangle. Join the mid-points of two imaginary class intervals, one on either side of the histogram, by line segments one after the other.

The histogram and a frequency polygon for a given data is as follows:

FRANK Solutions Class 9 Maths Chapter 23 - 10

11. Draw a histogram and a frequency polygon for the following data:

Wages

150 – 200

200 – 250

250 – 300

300 – 350

350 – 400

400 – 450

No. of workers

25

40

35

28

30

22

Solution:

We represent the class limits on the x-axis and the frequencies on the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, we construct rectangles to obtain a histogram of the given frequency distribution.

Now,

Take the mid-points of the upper horizontal side of each rectangle. Join the mid-points of two imaginary class intervals, one on either side of the histogram, by line segments one after the other.

Here, as the class limits do not start from 0, we put a kink between 0 and the lower

boundary of the first class.

The histogram and a frequency polygon of the given data is as follows

FRANK Solutions Class 9 Maths Chapter 23 - 11

12. Draw a frequency polygon for the following data:

Expenses

100 – 150

150 – 200

200 – 250

250 – 300

300 – 350

350 – 400

No. of families

22

37

26

18

10

5

Solution:

We take the class limits on the x-axis and the frequencies on the y-axis on suitable scales.

Now,

Find the class marks of all the class intervals. Locate the points (x1, y1) on the graph, where x1 denotes the class mark and y1 denotes the corresponding frequency. Join all the points plotted above with straight line segments. Join the first point and the last point to the points representing class marks of the class intervals before the first class interval and after the last class interval of the given frequency distribution.

Here, as the class limits do not start from 0, we put a kink between 0 and the lower boundary of the first class.

Frequency polygon for the given data is shown below

FRANK Solutions Class 9 Maths Chapter 23 - 12

13. Draw a frequency polygon for the following data:

Class

15 – 20

20 – 25

25 – 30

30 – 35

35 – 40

40 – 45

Frequency

5

12

15

26

18

7

Solution:

We take the class limits on the x-axis and the frequencies on the y-axis on suitable scales.

Now,

Find the class marks of all the class intervals. Locate the points (x1, y1) on the graph, where x1 denotes the class mark and y1 denotes the corresponding frequency. Join all the points plotted above with straight line segments. Join the first point and the last point to the points representing class marks of the class intervals before the first class interval and after the last class interval of the given frequency distribution

Here, as the class limits do not start from 0, we put a kink between 0 and the lower boundary of the first class

Frequency polygon for the given data is shown below

FRANK Solutions Class 9 Maths Chapter 23 - 13

14. Draw a frequency polygon for the following data:

Marks

5 – 9

10 – 14

15 – 19

20 – 24

25 – 29

30 – 34

No. of students

7

11

15

22

18

5

Solution:

We see that the class intervals are in an inclusive manner. We first need to convert them into exclusive manner.

Marks

No. of students

4.5 – 9.5

7

9.5 – 14.5

11

14.5 – 19.5

15

19.5 – 24.5

22

24.5 – 29.5

18

29.5 – 34.5

5

We take the class limits on the x-axis and the frequencies on the y-axis on suitable scales.

Now,

Find the class marks of all the class intervals. Locate the points (x1, y1) on the graph, where x1 denotes the class mark and y1 denotes the corresponding frequency. Join all the points plotted above with straight line segments. Join the first point and the last point to the points representing class marks of the class intervals before the first class interval and after the last class interval of the given frequency distribution.

Here, as the class limits do not start from 0, we put a kink between 0 and the lower boundary of the first class.

FRANK Solutions Class 9 Maths Chapter 23 - 14

15. Read the following bar graph and answer the following questions:

FRANK Solutions Class 9 Maths Chapter 23 - 15

a. What information is given by the graph?

b. Which state is the largest producer of wheat?

c. Which state is the largest producer of sugar?

d. Which state has total production of wheat and sugar as its maximum?

e. Which state has the total production of wheat and sugar minimum?

Solution:

a. The given graph gives information about production of wheat and sugar in five different states (U.P, Bihar, W.B, M.P, Punjab)

b. The largest producer of wheat is Punjab

c. The largest producer of sugar is U.P.

d. The state which has total production of wheat and sugar as its maximum is U.P.

e. The state which has total production of wheat and sugar minimum is W.B.

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