Exercise 7.2

1. Given below are the ages of 45 people in a colony:

33 8 7 25 31 26 5 50 25 48 56 33 28 22 15 62 59 16 14 19 24 35 26 9 12 46 15 42 63 32 5 22 11 42 23 52 48 62 10 24 43 51 37 48 36

Construct a grouped frequency distribution for the given data with 6 class intervals.

Solution:

Maximum value =

Minimum value =

Range= – =

Therefore, length of interval = 586 = = (Round off)

Then

Class Interval	Frequency
0-9
10-19
20-29
30-39
40-49
50-59
60-69

2. Number of students in 30 class rooms in a school are given below. Construct a frequency distribution table for the data with an exclusive class interval of 4 (students).

25 30 24 18 21 24 32 34 22 20 22 32 40 28 30 22 26 31 34 15 38 28 20 16 15 20 24 30 25 18

Solution:

Class number = 264 = = (Round off)

Class Interval	Frequency
15-22
23-30
31-38
39-46

3. Class intervals in a grouped frequency distribution are given as 4 – 11, 12 – 19, 20 – 27, 28 – 35, 36 – 43. Write the next two class intervals. (i) What is the length of each class interval? (ii) Write the class boundaries of all classes, (iii) What are the class marks of each class?

Solution:

Given distribution are

4 – 11, 12 – 19, 20 – 27, 28 – 35, 36 – 43

Next two distribution are – and – .

(i) Length of each class interval – =

(ii) Class boundaries: , , , ,

(iii)

Class Interval	Class Marks
4-11
12-19
20-27
28-35
36-43

4. In the following grouped frequency distribution table class marks are given.

Class Interval	Frequency
10	6
22	14
34	20
46	21
58	9
70	5

(i) Construct class intervals of the data(Exclusive class intervals)

(ii) Construct less than cumulative frequencies and

(iii) Construct greater than cumulative frequencies.

Solution:

(i) Class intervals of the data: 22 – 10 =

(ii) Class intervals are - , – , – , – , – , – .

Class	Frequency	Cumulative Frequency
Less than 16	6
Less than 28	14	+ =
Less than 40	20	+ =
Less than 52	21	+ =
Less than 64	9	+ =
Less than 76	5	+ =

(iii)

Class	Frequency	Cumulative Frequency
Greater than 6	75
Greater than 16	6	- =
Greater than 28	14	- =
Greater than 40	20	- =
Greater than 52	21	- =
Greater than 64	9	- =

5. The marks obtained by 35 students in a test in statistics (out of 50) are as below:

35 1 15 35 45 23 31 40 21 13 15 20 47 48 42 34 43 45 33 37 11 13 27 18 12 37 39 38 16 13 18 5 41 47 43

Construct a frequency distribution table with equal class intervals, one of them being 10-20 (20 is not included).

Solution:

Class	Distribution Frequency
0-10
10-20
20-30
30-40
40-50

6. Construct the class boundaries for the following frequency distribution table. Also construct less than cumulative and greater than cumulative frequency tables.

Ages	No of children
1 - 3	10
4 - 6	12
7 - 9	15
10 - 12	13
13 - 15	9

Solution:

Class	Frequency	Less than Cumulative	Greater than Cumulative
1 - 3
4 - 6
7 - 9
10 - 12
13 - 15

7. Cumulative frequency table is given below. Which type of cumulative frequency is given. Try to build the frequencies of respective class intervals.

Runs	No of cricketers
0 - 10	3
10 - 20	8
20 - 30	19
30 - 40	25
40 - 50	30

Solution:

Runs	No. of Students	Frequency
0 – 10	3	3
10 – 20		(8 – 3) =
20 – 30		(19 – 8) =
30 – 40		(25 – 19) =
40 – 50		(30 – 25) =

8. Number of readers in a library are given below. Write the frequency of respective classes. Also write the less than cumulative frequency table.

Number of books	Greater than Cumulative frequency
1-10	42
11-20	36
21-30	23
31-40	14
41-50	6

Solution:

No of Books	Frequency	Less than cumulative frequency
1 – 10	(42 – 36)
11 – 20	(36 – 23)	(6 + 13)
21 – 30	(23 – 14)	(19 + 9)
31 – 40	(14 – 6)	(28 + 8)
41 – 50		(36 + 6)

Chapter 7: Frequency Distribution Tables and Graphs

Glossary

Exercise 7.2

Sign in to Innings2

Chapter 7: Frequency Distribution Tables and Graphs

Reset Progress

Glossary

Exercise 7.2