EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Frequency Distribution
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
Given class interval
45
-
50
in exclusive form, its
class mark is
(i)
97
2
(ii)
189
4
(iii)
93
2
(iv)
48
(v)
95
2
Question
2
2.
Identify the cumulative frequency of the given grouped data.
class interval
26 - 36
37 - 47
48 - 58
59 - 69
70 - 80
81 - 91
92 - 102
frequency
8
15
20
20
22
20
20
(i)
class interval
Cumulative Frequency
26 - 36
8
37 - 47
28
48 - 58
43
59 - 69
63
70 - 80
85
81 - 91
105
92 - 102
125
(ii)
class interval
Cumulative Frequency
26 - 36
8
37 - 47
23
48 - 58
45
59 - 69
65
70 - 80
87
81 - 91
107
92 - 102
127
(iii)
class interval
Cumulative Frequency
26 - 36
8
37 - 47
23
48 - 58
43
59 - 69
59
70 - 80
81
81 - 91
101
92 - 102
121
(iv)
class interval
Cumulative Frequency
26 - 36
8
37 - 47
28
48 - 58
48
59 - 69
68
70 - 80
90
81 - 91
110
92 - 102
125
(v)
class interval
Cumulative Frequency
26 - 36
8
37 - 47
23
48 - 58
43
59 - 69
63
70 - 80
85
81 - 91
105
92 - 102
125
Question
3
3.
Given table in inclusive form, convert it into exclusive form.
Class-Interval
20 - 26
27 - 33
34 - 40
41 - 47
48 - 54
Frequency
38
17
28
42
14
(i)
Class-Interval
19.5 - 26.5
26.5 - 33.5
33.5 - 40.5
40.5 - 47.5
47.5 - 54.5
Frequency
38
17
28
42
14
(ii)
Class-Interval
19.5 - 25.5
26.5 - 32.5
33.5 - 39.5
40.5 - 46.5
47.5 - 53.5
Frequency
38
17
28
42
14
(iii)
Class-Interval
19.5 - 26
26.5 - 33
33.5 - 40
40.5 - 47
47.5 - 54
Frequency
38
17
28
42
14
(iv)
Class-Interval
20.5 - 26.5
27.5 - 33.5
34.5 - 40.5
41.5 - 47.5
48.5 - 54.5
Frequency
38
17
28
42
14
(v)
Class-Interval
20 - 26
26 - 32
32 - 38
38 - 44
44 - 50
Frequency
33
15
11
31
12
Question
4
4.
The marks obtained by
16
students in an examination are given below.
Represent the data in the form of a frequency distribution table
in inclusive form
taking class size
5
.
45
44
53
61
50
55
73
66
60
60
42
76
77
79
44
64
(i)
Marks
42 - 46
47 - 51
52 - 56
57 - 61
62 - 66
67 - 71
72 - 76
77 - 81
No. of Students
4
1
2
3
2
0
2
2
(ii)
Marks
42 - 46
47 - 51
52 - 56
57 - 61
62 - 66
67 - 71
72 - 76
77 - 81
No. of Students
4
1
3
2
2
0
2
2
(iii)
Marks
42 - 46
47 - 51
52 - 56
57 - 61
62 - 66
67 - 71
72 - 76
77 - 81
No. of Students
4
1
2
3
4
0
2
2
(iv)
Marks
42 - 46
47 - 51
52 - 56
57 - 61
62 - 66
67 - 71
72 - 76
77 - 81
No. of Students
4
2
2
3
2
0
2
1
(v)
Marks
42 - 46
47 - 51
52 - 56
57 - 61
62 - 66
67 - 71
72 - 76
77 - 81
No. of Students
4
1
4
3
2
0
2
2
Question
5
5.
The number of classes of class size
9
required to represent
the given random sample in exclusive form
3
5
6
9
10
11
11
15
16
17
23
26
27
29
29
32
32
33
35
35
36
40
44
47
48
(i)
7
(ii)
5
(iii)
4
(iv)
6
(v)
9
Question
6
6.
The following cumulative frequency table represents which of the following frequency distribution
Class-Interval
Cumulative Frequency
32 - 40
9
40 - 48
18
48 - 56
26
56 - 64
32
64 - 72
44
72 - 80
52
80 - 88
59
88 - 96
73
(i)
Class-Interval
32 - 40
40 - 48
48 - 56
56 - 64
64 - 72
72 - 80
80 - 88
88 - 96
Frequency
9
9
6
8
12
8
7
14
(ii)
Class-Interval
32 - 40
40 - 48
48 - 56
56 - 64
64 - 72
72 - 80
80 - 88
88 - 96
Frequency
9
14
8
6
12
8
7
9
(iii)
Class-Interval
32 - 40
40 - 48
48 - 56
56 - 64
64 - 72
72 - 80
80 - 88
88 - 96
Frequency
9
9
13
6
12
8
7
14
(iv)
Class-Interval
32 - 40
40 - 48
48 - 56
56 - 64
64 - 72
72 - 80
80 - 88
88 - 96
Frequency
9
9
8
6
15
8
7
14
(v)
Class-Interval
32 - 40
40 - 48
48 - 56
56 - 64
64 - 72
72 - 80
80 - 88
88 - 96
Frequency
9
9
8
6
12
8
7
14
Question
7
7.
The class boundaries of 33 - 35 which is in inclusive form are
(i)
32.5
-
35.5
(ii)
32
-
36
(iii)
32
-
35.5
(iv)
33
-
35
(v)
32.5
-
36
Question
8
8.
Identify the frequency distribution table for the given ages of 13 students in years
21
14
25
17
19
24
22
21
14
18
21
23
10
(i)
Age (in years)
10
14
17
18
19
21
22
23
24
25
No. of Students
1
2
1
2
1
2
1
1
1
1
(ii)
Age (in years)
10
14
17
18
19
21
22
23
24
25
No. of Students
1
2
1
1
1
2
1
1
2
1
(iii)
Age (in years)
10
14
17
18
19
21
22
23
24
25
No. of Students
1
2
1
1
1
3
1
1
1
1
(iv)
Age (in years)
10
11
12
14
15
16
19
21
22
24
No. of Students
2
1
2
1
1
1
2
1
1
1
(v)
Age (in years)
10
13
15
16
17
23
24
25
No. of Students
3
1
1
1
1
4
1
1
Question
9
9.
The daily wages (in rupees) of
19
workers in a factory are given below.
Represent the data in the form of a frequency distribution
in exclusive form
taking class size
30
.
280
237
219
248
239
217
216
283
275
283
220
293
293
244
250
203
210
299
240
(i)
Wages (in rupees)
203 - 233
233 - 263
263 - 293
293 - 323
No. of Workers
3
6
4
6
(ii)
Wages (in rupees)
203 - 233
233 - 263
263 - 293
293 - 323
No. of Workers
6
4
6
3
(iii)
Wages (in rupees)
203 - 233
233 - 263
263 - 293
293 - 323
No. of Workers
6
8
4
3
(iv)
Wages (in rupees)
203 - 233
233 - 263
263 - 293
293 - 323
No. of Workers
6
6
7
3
(v)
Wages (in rupees)
203 - 233
233 - 263
263 - 293
293 - 323
No. of Workers
6
6
4
3
Question
10
10.
The class marks of a frequency distribution are
12.5 , 17.5 , 22.5 , 27.5
.
Find the class size and class intervals
in exclusive form
(i)
5
;
10
-
15
,
15
-
20
,
20
-
25
,
25
-
30
(ii)
5
;
11
-
16
,
16
-
21
,
21
-
26
,
26
-
31
(iii)
6
;
10
-
15
,
16
-
21
,
22
-
27
,
28
-
33
(iv)
5
;
9
-
14
,
14
-
19
,
19
-
24
,
24
-
29
(v)
7
;
9
-
15
,
16
-
22
,
23
-
29
,
30
-
36
Question
11
11.
Which of the following are continuous variables?
a)
Population of cities
b)
Marks obtained by student in a particular subject
c)
Rainfall at a place over a month
d)
Number of members in a family
e)
Temperature at a place over a month
(i)
{c,e}
(ii)
{b,e,c}
(iii)
{a,c}
(iv)
{d,a,c}
(v)
{b,e}
Question
12
12.
Given class interval
48
-
52
in exclusive form, its
mid value is
(i)
49
(ii)
51
(iii)
50
(iv)
53
(v)
47
Question
13
13.
If the length of the class is 4, then the number of class intervals needed to represent data with range 30 is
(i)
10
(ii)
7
(iii)
9
(iv)
6
(v)
8
Question
14
14.
The sale of shirts of various sizes at a shop on a particular day is given below. Identify the frequency distribution table for the given data.
33
31
37
34
20
23
24
30
38
36
39
29
28
30
20
36
24
24
(i)
Size
20
23
24
28
29
30
31
33
34
36
37
38
39
No. of Shirts
1
1
3
1
1
2
1
1
2
2
1
1
1
(ii)
Size
20
23
24
28
29
30
31
33
34
36
37
38
39
No. of Shirts
2
1
4
1
1
1
1
1
1
2
1
1
1
(iii)
Size
20
21
23
25
26
27
28
29
31
32
33
37
40
No. of Shirts
1
2
2
2
2
1
1
2
1
1
1
1
1
(iv)
Size
20
23
24
28
29
30
31
33
34
36
37
38
39
No. of Shirts
2
1
3
1
1
2
1
1
1
2
1
1
1
(v)
Size
20
23
24
25
27
28
31
33
35
36
39
40
No. of Shirts
4
3
2
1
1
1
1
1
1
1
1
1
Question
15
15.
Given the sample data, prepare the class interval table in
inclusive
form with
3
as min value and a class size of
5
.
10
23
48
20
21
42
6
20
34
50
35
15
31
16
18
33
3
20
30
4
(i)
Class-Interval
3 - 7
8 - 12
13 - 17
18 - 22
23 - 27
28 - 32
33 - 37
38 - 42
43 - 47
48 - 52
Frequency
3
2
1
5
1
2
3
1
0
2
(ii)
Class-Interval
3 - 7
8 - 12
13 - 17
18 - 22
23 - 27
28 - 32
33 - 37
38 - 42
43 - 47
48 - 52
Frequency
3
1
5
2
1
2
3
1
0
2
(iii)
Class-Interval
3 - 7
8 - 12
13 - 17
18 - 22
23 - 27
28 - 32
33 - 37
38 - 42
43 - 47
48 - 52
Frequency
3
1
2
5
1
2
3
1
0
2
(iv)
Class-Interval
3 - 7
8 - 12
13 - 17
18 - 22
23 - 27
28 - 32
33 - 37
38 - 42
43 - 47
48 - 52
Frequency
3
1
2
3
1
2
3
1
0
2
(v)
Class-Interval
3 - 8
8 - 13
13 - 18
18 - 23
23 - 28
28 - 33
33 - 38
38 - 43
43 - 48
48 - 53
Frequency
3
1
2
5
1
2
3
1
0
2
Question
16
16.
Given the sample data, prepare the class interval table in
exclusive
form with
1
as min value and a class size of
10
.
17
9
28
3
7
31
1
40
37
8
16
20
43
29
46
19
24
35
34
(i)
Class-Interval
1 - 11
11 - 21
21 - 31
31 - 41
41 - 51
Frequency
5
2
3
5
4
(ii)
Class-Interval
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
Frequency
5
4
3
5
2
(iii)
Class-Interval
1 - 11
11 - 21
21 - 31
31 - 41
41 - 51
Frequency
5
8
3
5
2
(iv)
Class-Interval
1 - 11
11 - 21
21 - 31
31 - 41
41 - 51
Frequency
5
3
4
5
2
(v)
Class-Interval
1 - 11
11 - 21
21 - 31
31 - 41
41 - 51
Frequency
5
4
3
5
2
Question
17
17.
Given class interval
14
-
20
in exclusive form, its
class size is
(i)
5
(ii)
7
(iii)
4
(iv)
8
(v)
6
Question
18
18.
In exclusive form representation, the observation
26
falls in which class?
(i)
26
-
36
(ii)
16
-
26
(iii)
31
-
41
(iv)
21
-
26
(v)
36
-
46
Question
19
19.
The true lower limit and true upper limit of the class with frequency x is
Class-Interval
Frequency
13 - 20
27
21 - 28
x
29 - 36
30
37 - 44
12
45 - 52
12
(i)
20.5
-
28.5
(ii)
21
-
28
(iii)
20
-
29
(iv)
20
-
28.5
(v)
20.5
-
29
Question
20
20.
Which of the following class intervals are in inclusive form?
a)
14 - 20 , 20 - 26 , 26 - 32,...
b)
14 - 20 , 21 - 27 , 28 - 34,...
c)
35 - 41 , 42 - 48 , 49 - 55,...
d)
32 - 38 , 38 - 44 , 44 - 50...
e)
13.5 - 20.5 , 20.5 - 27.5 , 27.5 - 34.5...
(i)
{d,c}
(ii)
{d,c,b}
(iii)
{a,b}
(iv)
{e,a,b}
(v)
{b,c}
Question
21
21.
Find the sum of frequencies for the given table
Value
10
27
42
59
60
61
71
76
84
Frequency
1
1
1
1
1
1
1
1
2
(i)
9
(ii)
11
(iii)
7
(iv)
10
(v)
13
Question
22
22.
The class boundaries of 33 - 35 which is in exclusive form are
(i)
32.5
-
35
(ii)
32.5
-
35.5
(iii)
33
-
35.5
(iv)
33
-
35
(v)
33.5
-
34.5
Question
23
23.
Given class interval table, find the sum of frequencies.
Class-Interval
14 - 23
23 - 32
32 - 41
41 - 50
50 - 59
59 - 68
68 - 77
77 - 86
Frequency
8
30
9
12
23
28
17
29
(i)
157
(ii)
153
(iii)
158
(iv)
155
(v)
156
Question
24
24.
Which of the following are discontinuous variables?
a)
Weights of persons in a group.
b)
Wages of workers in a factory.
c)
Number of workers in a factory.
d)
Number of members in a family.
e)
Heights of children in a class.
(i)
{c,d}
(ii)
{b,d,c}
(iii)
{e,a,c}
(iv)
{a,c}
(v)
{b,d}
Question
25
25.
The marks obtained by
15
students in an examination are given below.
Represent the data in the form of a frequency distribution table
in exclusive form
taking class size
6
.
40
51
75
70
52
78
42
42
46
48
58
54
65
68
44
(i)
Marks
40 - 46
46 - 52
52 - 58
58 - 64
64 - 70
70 - 76
76 - 82
No. of Students
4
3
2
3
2
2
1
(ii)
Marks
40 - 46
46 - 52
52 - 58
58 - 64
64 - 70
70 - 76
76 - 82
No. of Students
4
1
2
1
2
2
3
(iii)
Marks
40 - 46
46 - 52
52 - 58
58 - 64
64 - 70
70 - 76
76 - 82
No. of Students
4
3
5
1
2
2
1
(iv)
Marks
40 - 46
46 - 52
52 - 58
58 - 64
64 - 70
70 - 76
76 - 82
No. of Students
4
3
2
1
2
2
1
(v)
Marks
40 - 46
46 - 52
52 - 58
58 - 64
64 - 70
70 - 76
76 - 82
No. of Students
4
2
3
1
2
2
1
Assignment Key
1) (v)
2) (v)
3) (i)
4) (i)
5) (iv)
6) (v)
7) (i)
8) (iii)
9) (v)
10) (i)
11) (i)
12) (iii)
13) (v)
14) (iv)
15) (iii)
16) (v)
17) (v)
18) (i)
19) (i)
20) (v)
21) (iv)
22) (iv)
23) (v)
24) (i)
25) (iv)
