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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

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