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

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

Chapter Name	RD Sharma Chapter 22 Tabular Representation of Statistical Data Exercise 22.2
Book Name	RD Sharma Mathematics for Class 10
Other Exercises	Exercise 22.1
Related Study	NCERT Solutions for Class 10 Maths

Exercise 22.2 Solutions

1. Define cumulative frequency distribution.

Solution

Cumulative frequency distribution: A table which displays the manner in which cumulative frequencies are distributed over various classes is called a cumulative frequencies (or) cumulative frequencies distribution table.

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

Solution

Frequencies table or frequency distribution is a method to represent raw data in the form from which one can easily understand the information contained in a raw data , where as a table which plays the manner in which cumulative frequencies are distributed over various classes is called a cumulative frequency distribution.

3. The marks scored 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

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

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 resent the data as a cumulative frequency table using 70-79 as one of

the class intervals.

Solution

The minimum bill is Rs 24. 
Maximum bill is Rs 95. 
Range = Maximum bill - minimum bill 

= 95 - 24 = 71 
Given class in terval is 70 - 79, So class size 

= 79 - 70 = 9 
∴ Number of classes = Range/class size = 71/9 = 7.88
∴ Number of classes = 8 
The cumulative frequency distribution table is as 

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

Minimum number of book shelves is 16 and maximum number of book shelves is 45 
Range = maximum B.S - Minimum B.S

= 45 - 16 = 29 
Given class interval = 45 - 49. So class size 
= 49 - 45 = 4 
∴ Number of classes = Range/Class size = 29/4 = 7.25
⇒ Number of classes = 8. 
The cumulative frequencies distribution is as 

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

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 360	24
Below 390	38
Below 420	40

(i) Represent this as a frequency distribution table. 

(ii) Prepare a cumulative frequency table. 

Solution

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

Ace 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