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# Chapter 22: Tabular Representation of Statistical Data Exercise – 22.2

### Question: 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 frequency distribution or cumulative frequency distribution table.

### Question: 2

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

### Solution:

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.

### 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 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

### 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 table.

### Solution:

 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

### Question: 5

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:

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 = Range/class size = 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

### Question: 6

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:

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 = Range/class size = 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

### 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 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:

 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

### 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

(1) Represent this as a frequency distribution table.

(2) Prepare a cumulative frequency table.

### Solution:

(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

### Question: 9

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:

 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