RD Sharma Solutions Class 9 Tabular Representation Of Statistical Data Exercise 22.2

RD Sharma Class 9 Solutions Chapter 22 Ex 22.2 Free Download

RD Sharma Solutions Class 9 Chapter 22 Exercise 22.2

Q1. Define cumulative frequency distribution.

Solution 1: Cumulative frequency distribution:

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

Q2. Explain the difference between a frequency distribution and a cumulative frequency distribution.

Solution 2:

Frequency 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.

Q3. 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 3:

Marks No. of students Marks Cumulative Frequency
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  

Q4. 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 table.

Solution 4:

Age (in years) No. of students Marks Cumulative Frequency
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    

Q5. The water bills (in rupees) of 32 houses in a certain street for the period 1.198 to 31.398 are given below:

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

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

Solution 5:

The minimum bill is Rs 24

The maximum bill is Rs 95

Range=Maximum bill-Minimum bill=95-24=71

Given class interval is 70-79.So, class size=79-70=9

Therefore number of classes= \(\frac{Range}{class size}\)= \(\frac{71}{9}\)=7.80

Number of classes=8

The cumulative frequency distribution is as follows:

Bills No. of houses(frequency) Cumulative frequency
16-25 1 1
25-34 3 4
34-43 5 9
43-52 4 13
52-61 7 20
61-70 6 26
70-79 3 29
79-88 2 31
88-97 1 32

Q6.The number of books in different shelves of a library is 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 6:

The minimum number of bookshelves is 16

and maximum number of bookshelves is 45

Range=Maximum book shelves-Minimum book shelves=45-16=29

Given class interval is 45-49.So, class size=49-45=4

Therefore number of classes= \(\frac{Range}{class size}\)= \(\frac{29}{4}\)==7.25

Number of classes=8

The cumulative frequency distribution is as follows:

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 60

Q7. 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 30 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 7:

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 60-65 671-621=53
Below 70 685 65-70 685-671=11

Q8. 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

(1) Represent this as a frequency distribution table.

(2)Prepare a cumulative frequency table.

Solution 8:

(1)

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

(2)

Class interval Frequency Consumption(in KW) No. of factories
0-240 1 More than 0 40
240-270 3 More than 240 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    

Q9. Given below is a cumulative frequency distribution table showing ages of the people living in a locality:

Age in years No. of years
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 9:

Age (in years) No. of persons Class interval Frequency
Above 0 1124 0-12 1124-1026=98
Above 12 1026 12-24 217
Above 24 809 24-36 382
Above  36 427 36-48 269
Above 38 158 48-60 138
Above 60 20 60-72 15
Above 72 5 72-84 5-3=2
Above 84 3 84-96 3-1=2
Above 96 3 96-108 1-0=1

Leave a Comment

Your email address will not be published. Required fields are marked *