EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Frequency Distribution
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
Convert the discontinuous form of the class interval 34 - 37 to continuous form
(i)
33
-
38
(ii)
34
-
37
(iii)
33.5
-
38
(iv)
33
-
37.5
(v)
33.5
-
37.5
Question
2
2.
The following cumulative frequency table represents which of the following frequency distribution
Class-Interval
Cumulative Frequency
14 - 18
12
18 - 22
19
22 - 26
29
26 - 30
42
30 - 34
49
34 - 38
56
(i)
Class-Interval
14 - 18
18 - 22
22 - 26
26 - 30
30 - 34
34 - 38
Frequency
12
7
10
13
7
7
(ii)
Class-Interval
14 - 18
18 - 22
22 - 26
26 - 30
30 - 34
34 - 38
Frequency
12
10
7
13
7
7
(iii)
Class-Interval
14 - 18
18 - 22
22 - 26
26 - 30
30 - 34
34 - 38
Frequency
12
7
8
13
7
7
(iv)
Class-Interval
14 - 18
18 - 22
22 - 26
26 - 30
30 - 34
34 - 38
Frequency
12
7
10
8
7
7
Question
3
3.
The class size used in the below table is
Class-Interval
32 - 38
38 - 44
44 - 50
50 - 56
56 - 62
62 - 68
68 - 74
Frequency
17
12
19
7
10
18
25
(i)
6
(ii)
7
(iii)
4
(iv)
5
(v)
8
Question
4
4.
The lower limit of the class with frequency x is
Class-Interval
Frequency
35 - 43
21
44 - 52
2
53 - 61
21
62 - 70
x
71 - 79
10
(i)
61
(ii)
60
(iii)
62
(iv)
65
(v)
63
Question
5
5.
The class marks of a frequency distribution are
20 , 29 , 38 , 47
.
Find the class size and class intervals
in inclusive form
(i)
9
;
16
-
24
,
25
-
33
,
34
-
42
,
43
-
51
(ii)
9
;
17
-
25
,
26
-
34
,
35
-
43
,
44
-
52
(iii)
9
;
15
-
23
,
24
-
32
,
33
-
41
,
42
-
50
(iv)
8
;
16
-
24
,
24
-
32
,
32
-
40
,
40
-
48
(v)
9
;
15
-
24
,
24
-
33
,
33
-
42
,
42
-
51
Question
6
6.
Which of the following are discontinuous variables?
a)
Wages of workers in a factory.
b)
Number of workers in a factory.
c)
Number of members in a family.
d)
Heights of children in a class.
e)
Weights of persons in a group.
(i)
{e,a,b}
(ii)
{d,c,b}
(iii)
{a,b}
(iv)
{b,c}
(v)
{d,c}
Question
7
7.
Given the sample data, prepare the class interval table in
exclusive
form with
2
as min value and a class size of
5
.
15
29
46
23
49
31
10
14
2
27
19
46
27
42
26
31
(i)
Class-Interval
2 - 7
7 - 12
12 - 17
17 - 22
22 - 27
27 - 32
32 - 37
37 - 42
42 - 47
47 - 52
Frequency
1
1
2
4
2
5
0
0
3
1
(ii)
Class-Interval
2 - 7
7 - 12
12 - 17
17 - 22
22 - 27
27 - 32
32 - 37
37 - 42
42 - 47
47 - 52
Frequency
1
1
2
1
2
5
0
0
3
1
(iii)
Class-Interval
2 - 7
7 - 12
12 - 17
17 - 22
22 - 27
27 - 32
32 - 37
37 - 42
42 - 47
47 - 52
Frequency
1
2
1
1
2
5
0
0
3
1
(iv)
Class-Interval
2 - 7
7 - 12
12 - 17
17 - 22
22 - 27
27 - 32
32 - 37
37 - 42
42 - 47
47 - 52
Frequency
1
1
1
2
2
5
0
0
3
1
(v)
Class-Interval
2 - 6
7 - 11
12 - 16
17 - 21
22 - 26
27 - 31
32 - 36
37 - 41
42 - 46
47 - 51
Frequency
1
1
2
1
2
5
0
0
3
1
Question
8
8.
If the upper and lower limit of class interval are 19 and 16 respectively, then the class interval is
(i)
15.5
-
19.5
(ii)
16
-
19
(iii)
16.5
-
18.5
(iv)
15.5
-
19
(v)
16
-
19.5
Question
9
9.
The number of classes of class size
10
required to represent
the given random sample in exclusive form
4
4
5
8
10
10
10
15
17
17
18
20
22
26
26
28
30
36
37
38
40
41
41
41
44
44
45
46
47
47
49
49
(i)
4
(ii)
6
(iii)
2
(iv)
8
(v)
5
Question
10
10.
Identify the cumulative frequency of the given grouped data.
class interval
22 - 32
33 - 43
44 - 54
55 - 65
66 - 76
frequency
11
10
16
20
22
(i)
class interval
Cumulative Frequency
22 - 32
11
33 - 43
27
44 - 54
37
55 - 65
57
66 - 76
79
(ii)
class interval
Cumulative Frequency
22 - 32
11
33 - 43
19
44 - 54
35
55 - 65
55
66 - 76
77
(iii)
class interval
Cumulative Frequency
22 - 32
11
33 - 43
33
44 - 54
49
55 - 65
69
66 - 76
79
(iv)
class interval
Cumulative Frequency
22 - 32
11
33 - 43
21
44 - 54
40
55 - 65
60
66 - 76
82
(v)
class interval
Cumulative Frequency
22 - 32
11
33 - 43
21
44 - 54
37
55 - 65
57
66 - 76
79
Question
11
11.
Which of the following are continuous variables?
a)
Marks obtained by student in a particular subject
b)
Rainfall at a place over a month
c)
Number of workers in a factory
d)
Temperature at a place over a month
e)
Number of players in a team
(i)
{e,a,b}
(ii)
{b,d}
(iii)
{a,b}
(iv)
{c,d}
(v)
{c,d,b}
Question
12
12.
The following outcomes were noted when a dice was thrown 20 times. Identify the frequency distribution table for the given data.
1
2
5
6
1
1
4
3
5
6
6
3
3
2
4
4
2
1
2
3
(i)
Outcome
1
2
3
4
5
6
No. of outcomes
2
4
3
4
3
4
(ii)
Outcome
1
2
3
4
5
6
No. of outcomes
3
1
1
7
1
7
(iii)
Outcome
1
2
3
4
5
6
No. of outcomes
5
3
4
3
2
3
(iv)
Outcome
1
2
3
4
5
6
No. of outcomes
4
4
4
3
2
3
Question
13
13.
Construct a frequency distribution table from the following cumulative frequency distribution
Class-Interval
Cumulative Frequency
37 - 43
12
44 - 50
17
51 - 57
23
58 - 64
35
65 - 71
49
72 - 78
56
(i)
Class-Interval
37 - 43
44 - 50
51 - 57
58 - 64
65 - 71
72 - 78
Frequency
12
5
6
9
14
7
(ii)
Class-Interval
37 - 43
44 - 50
51 - 57
58 - 64
65 - 71
72 - 78
Frequency
12
5
6
12
14
7
(iii)
Class-Interval
37 - 43
44 - 50
51 - 57
58 - 64
65 - 71
72 - 78
Frequency
12
5
3
12
14
7
(iv)
Class-Interval
37 - 43
44 - 50
51 - 57
58 - 64
65 - 71
72 - 78
Frequency
12
7
6
12
14
5
(v)
Class-Interval
37 - 43
44 - 50
51 - 57
58 - 64
65 - 71
72 - 78
Frequency
12
6
5
12
14
7
Question
14
14.
The class boundaries of 12 - 15 which is in exclusive form are
(i)
12.5
-
14.5
(ii)
11.5
-
15
(iii)
12
-
15
(iv)
12
-
15.5
(v)
11.5
-
15.5
Question
15
15.
Arrange the following data
17
34
30
22
30
40
36
13
23
30
in ascending order
(i)
13
17
22
23
30
30
30
34
36
40
(ii)
40
17
18
18
28
38
13
38
22
39
(iii)
22
18
18
24
38
40
25
26
26
26
(iv)
26
17
22
32
35
39
11
19
25
24
(v)
32
26
28
36
14
38
20
17
30
33
Question
16
16.
Which of the following class intervals are in inclusive form?
a)
24.5 - 33.5 , 33.5 - 42.5 , 42.5 - 51.5...
b)
49 - 57 , 57 - 65 , 65 - 73...
c)
52 - 60 , 61 - 69 , 70 - 78,...
d)
25 - 33 , 34 - 42 , 43 - 51,...
e)
25 - 33 , 33 - 41 , 41 - 49,...
(i)
{c,d}
(ii)
{b,d}
(iii)
{b,d,c}
(iv)
{e,a,c}
(v)
{a,c}
Question
17
17.
Which of the following are true?
a)
Each numerical figure in a data set is called an observation.
b)
The difference between the true upper limit and true lower limit is called the class mark.
c)
The true lower limit of the inclusive form class interval 30 - 40 is 30.
d)
The true lower limit of the exclusive form class interval 30 - 40 is 30.
e)
The number of times a particular observation occurs is called its frequency.
(i)
{a,d,e}
(ii)
{c,d}
(iii)
{b,c,e}
(iv)
{b,a}
(v)
{b,a,d}
Question
18
18.
The mid value of the class with frequency x is
Class-Interval
Frequency
4 - 14
20
14 - 24
x
24 - 34
7
34 - 44
3
44 - 54
19
(i)
19
(ii)
20
(iii)
18
(iv)
21
(v)
16
Question
19
19.
The marks obtained by
17
students in an examination are given below.
Represent the data in the form of a frequency distribution table
in exclusive form
taking class size
5
.
53
51
57
60
41
66
68
70
71
67
48
57
55
75
69
42
47
(i)
Marks
41 - 46
46 - 51
51 - 56
56 - 61
61 - 66
66 - 71
71 - 76
No. of Students
2
3
2
3
0
5
2
(ii)
Marks
41 - 46
46 - 51
51 - 56
56 - 61
61 - 66
66 - 71
71 - 76
No. of Students
2
2
3
7
0
5
2
(iii)
Marks
41 - 46
46 - 51
51 - 56
56 - 61
61 - 66
66 - 71
71 - 76
No. of Students
2
2
3
3
0
5
2
(iv)
Marks
41 - 46
46 - 51
51 - 56
56 - 61
61 - 66
66 - 71
71 - 76
No. of Students
2
2
8
3
0
5
2
Question
20
20.
The marks obtained by
19
students in an examination are given below.
Represent the data in the form of a frequency distribution table
in exclusive form
taking class size
5
.
60
70
69
75
53
41
77
43
71
57
80
42
76
71
47
49
59
40
47
(i)
Marks
40 - 45
45 - 50
50 - 55
55 - 60
60 - 65
65 - 70
70 - 75
75 - 80
80 - 85
No. of Students
4
3
1
2
4
1
3
3
1
(ii)
Marks
40 - 45
45 - 50
50 - 55
55 - 60
60 - 65
65 - 70
70 - 75
75 - 80
80 - 85
No. of Students
4
3
1
2
1
1
3
3
1
(iii)
Marks
40 - 45
45 - 50
50 - 55
55 - 60
60 - 65
65 - 70
70 - 75
75 - 80
80 - 85
No. of Students
4
3
2
1
1
1
3
3
1
(iv)
Marks
40 - 45
45 - 50
50 - 55
55 - 60
60 - 65
65 - 70
70 - 75
75 - 80
80 - 85
No. of Students
4
3
1
7
1
1
3
3
1
(v)
Marks
40 - 45
45 - 50
50 - 55
55 - 60
60 - 65
65 - 70
70 - 75
75 - 80
80 - 85
No. of Students
4
1
1
2
1
1
3
3
3
Question
21
21.
The daily wages (in rupees) of
20
workers in a factory are given below.
Represent the data in the form of a frequency distribution
in exclusive form
taking class size
30
.
218
236
230
249
211
258
261
298
250
254
223
259
245
292
256
251
221
268
223
272
(i)
Wages (in rupees)
211 - 241
241 - 271
271 - 301
No. of Workers
7
13
3
(ii)
Wages (in rupees)
211 - 241
241 - 271
271 - 301
No. of Workers
7
10
3
(iii)
Wages (in rupees)
211 - 241
241 - 271
271 - 301
No. of Workers
10
7
3
(iv)
Wages (in rupees)
211 - 241
241 - 271
271 - 301
No. of Workers
3
10
7
(v)
Wages (in rupees)
211 - 241
241 - 271
271 - 301
No. of Workers
7
5
3
Question
22
22.
The true lower limit and true upper limit of the class with frequency x is
Class-Interval
Frequency
20 - 28
6
28 - 36
22
36 - 44
24
44 - 52
x
52 - 60
30
(i)
43.5
-
52.5
(ii)
43.5
-
52
(iii)
44
-
52
(iv)
44
-
52.5
(v)
44.5
-
51.5
Question
23
23.
The number of children in 18 families are given below. Identify the frequency distribution table for the given data.
4
4
4
5
5
5
0
5
5
4
5
3
1
1
0
3
4
5
(i)
No. of children
0
1
2
3
4
5
No. of families
2
2
2
4
4
4
(ii)
No. of children
0
1
2
3
4
5
No. of families
4
2
2
3
4
3
(iii)
No. of children
0
1
3
4
5
No. of families
2
2
2
6
6
(iv)
No. of children
0
1
3
4
5
No. of families
2
2
1
6
7
(v)
No. of children
0
1
3
4
5
No. of families
2
2
2
5
7
Question
24
24.
Identify the cumulative frequency of the given grouped data.
class interval
10 - 17
17 - 24
24 - 31
31 - 38
38 - 45
45 - 52
52 - 59
frequency
22
23
15
11
19
21
6
(i)
class interval
Cumulative Frequency
10 - 17
22
17 - 24
45
24 - 31
57
31 - 38
68
38 - 45
87
45 - 52
108
52 - 59
114
(ii)
class interval
Cumulative Frequency
10 - 17
22
17 - 24
45
24 - 31
60
31 - 38
71
38 - 45
90
45 - 52
111
52 - 59
117
(iii)
class interval
Cumulative Frequency
10 - 17
22
17 - 24
37
24 - 31
60
31 - 38
71
38 - 45
90
45 - 52
111
52 - 59
117
(iv)
class interval
Cumulative Frequency
10 - 17
22
17 - 24
28
24 - 31
43
31 - 38
54
38 - 45
73
45 - 52
94
52 - 59
117
(v)
class interval
Cumulative Frequency
10 - 17
22
17 - 24
45
24 - 31
60
31 - 38
66
38 - 45
85
45 - 52
106
52 - 59
112
Question
25
25.
During the medical check-up of 44 students of a class, their weights in kgs are recorded as follows.
Identify the number of students whose weight is more than 45 kg
Class-Interval
38 - 45
45 - 52
52 - 59
59 - 66
66 - 73
Frequency
12
6
10
7
9
(i)
32
(ii)
33
(iii)
29
(iv)
31
(v)
35
Assignment Key
1) (v)
2) (i)
3) (i)
4) (iii)
5) (i)
6) (iv)
7) (ii)
8) (ii)
9) (v)
10) (v)
11) (ii)
12) (iv)
13) (ii)
14) (iii)
15) (i)
16) (i)
17) (i)
18) (i)
19) (iii)
20) (ii)
21) (ii)
22) (iii)
23) (v)
24) (ii)
25) (i)
