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