Class 9 RD Sharma Solutions – Chapter 22 Tabular Representation of Statistical Data – Exercise 22.2

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