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Class 9 RD Sharma Solutions – Chapter 22 Tabular Representation of Statistical Data – Exercise 22.2
  • Last Updated : 18 Mar, 2021

Question 1. Define cumulative frequency distribution.

Solution:

The structure showing the distribution of cumulative frequencies over various classes is known as cumulative frequency distribution.

Question 2. Explain the difference between a frequency distribution and a cumulative frequency distribution.

Solution:

The method representing raw data which is easily understandable is called frequency distribution. The structure showing the distribution of cumulative frequencies over various classes is known as cumulative frequency distribution.

Question 3. The marks scored by 55 students in a test are given below:

Marks



0-5

5-10

10-15

15-20

20-25

25-30

30-35

No. of students



2

6

13

17

11

4

2

Prepare a cumulative frequency table.

Solution:

Marks

No. of students



Marks

No. of students

0-5

2

Less than 5

2

5-10

6

Less than 10

8

10-15

13

Less than 15

21

15-20

17

Less than 20

38

20-25

11

Less than 25

49

25-30

4

Less than 30

53

30-35

2

Less than 35

55

 

N = 55

 

 

Question 4. Following are the ages of 360 patients getting medical treatment in a hospital on a day:

Age (in years)

10-20

20-30

30-40

40-50

50-60

60-70

No. of Patients

90

50

60

80

50

30

Construct a cumulative frequency distribution.

Solution:

Age (in years)

No. of patients

Age (in years)

No. of patients

10-20

90

Less than 20

90

20-30

50

Less than 30

140

30-40

60

Less than 40

200

40-50

80

Less than 50

280

50-60

50

Less than 60

330

60-70

30

Less than 70

360

 

N = 360

 

 

Question 5. The water bills (in rupees) of 32 houses in a certain street for the period 1.1.98 to 31.3.98 are given below : 

56, 43, 32, 38, 56, 24, 68, 85, 52, 47, 35, 58, 63, 74, 27, 84, 69, 35, 44, 75, 55, 30, 54, 65, 45, 67, 95, 72, 43, 65, 35, 59.

Tabulate the data and present the data as a cumulative frequency table using 70-79 as one of the class intervals. 

Solution: 

The minimum and maximum bills are Rs 24 and Rs 95 respectively. 

Range of the class interval is 95-24 = 71.

Class interval given = 70-79, with the class size being 9. 

number of classes = range/class-size = 71/9 = 7.80 which is approximately 8. 

Cumulative frequency distribution is as follows : 

Bills (Rs.)

No. of houses(Frequency)

16-25

1

25-34

3

34-43

5

43-52

4

52-61

7

61-70

6

70-79

3

79-88

2

88-97

1

Question 6. The number of books in different shelves of a library are as follows : 

30, 32, 28, 24, 20, 25, 38, 37, 40, 45, 16, 20, 19, 24, 27, 30, 32, 34, 35, 42, 27, 28, 19, 34, 38, 39, 42, 29, 24, 27, 22, 29, 31, 19, 27, 25, 28, 23, 24, 32, 34, 18, 27, 25, 37, 31, 24, 23, 43, 32, 28, 31, 24, 23, 26, 36, 32, 29, 28, 21.

Prepare a cumulative frequency distribution table using 45-49 as the last class interval. 

Solution: 

The minimum and maximum book shelves are 16 and 45 respectively. 

The range of the book shelves 45-16 = 29

We have the following class interval , 45 – 49, with the class size =4.

Number of classes = Range/Class size = 29/4 = 7.25 , which approximates to 8 nearly.

No. of books

No. of shelves  (Frequency)

Cumulative Frequency

13-17

1

1

17-21

6

7

21-25

11

18

25-29

15

33

29-33

12

45

33-37

5

50

37-41

6

56

41-45

3

59

45-49

1

50

Question 7. Given below are the cumulative frequencies showing the weights of 685 students of a school. Prepare a frequency distribution table. 

Weight (in kg)

No. of students

Below 25

0

Below 30

24

Below 35

78

Below 40

183

Below 45

294

Below 50

408

Below 55

543

Below 60

621

Below 65

674

Below 70

685

Solution: 

Weight (in kg)

No. of students

Class interval 

Frequency

Below 30

24

25-30

24 – 0 =24

Below 35

78

30-35

78- 24 = 54

Below 40

183

35-40

183 – 78 = 105

Below 45

294

40-45

294 – 183 = 111

Below 50

408

45-50

408 – 294 = 114

Below 55

543

50-55

543 – 408 = 135

Below 60

621

55-60

621 – 543 = 78

Below 65

674

60-65

674 – 621 = 53

Below 70

685

65-70

685 – 674 = 11

Question 8. The following cumulative frequency distribution table shows the daily electricity consumption (in kW) of 40 factories in an industrial state:

Consumption (in kW)

No. of factories

Below 240

1

Below 270

4

Below 300

8

Below 330

24

Below 360

33

Below 390

38

Below 420

40

(i) Represent this as a frequency distribution table.

(ii) Prepare a cumulative frequency table.

Solution: 

(i) 

Consumption (in kW)

No. of factories

Class interval

Frequency

Below 240

1

0-240

1

Below 270

4

240-270

4-1 = 3

Below 300

8

270-300

8-4 = 4

Below 330

24

300-330

24-8 = 16

Below 360

33

330-360

33 – 24 = 9

Below 390

38

360-390

38-33 = 5

Below 420

40

390-420

40-38 = 2

(ii)

Class interval

Frequency

Consumption (in kW)

No. of factories

0-240

1

More than 0

40

240-270

3

More than 270

40-1 = 39

270-300

4

More than 270

39-3 = 36

300-330

16

More than 300

36-4 = 32

330-360

9

More than 330

32-16= 16

360-390

5

More than 360

16-9 = 7

390-420

2

More than 390

7-5=2

 

 

More than 420

2-2 = 0

 

N = 40

 

 

Question 9. Given below is a cumulative frequency distribution table showing ages of people living in a locality:

Age in years

No. of persons

Above 108

0

Above 96

1

Above 84

3

Above 72

5

Above 60

20

Above 48

158

Above 36

427

Above 24

809

Above 12

1026

Above 0

1124

Prepare a frequency distribution table.

Solution:

Age (in years)

No. of persons

Class interval

Frequency

Above 0 

1124

0-12

1124-1026 = 98

Above 12

1026

12-24

1026-809 = 217

Above 24

809

24-36

809-427 = 382

Above 36

427

36-48

427-158= 269

Above 48

158

48-60

158-20 = 138

Above 60

20

60-72

20 -5 = 15

Above 72

5

72-84

5-3 = 2

Above 84

3

84-96

3-1 = 2

Above 96

1

96-108

1-0 = 1

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