Class 9 RD Sharma Solutions Chapter 22 Tabular Representation of Statistical Data Exercise 22.2 (original) (raw)

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