EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Frequency Distribution
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
During the medical check-up of 66 students of a class, their weights in kgs are recorded as follows.
Identify the number of students whose weight is more than 75 kg
Class-Interval
39 - 45
45 - 51
51 - 57
57 - 63
63 - 69
69 - 75
75 - 81
81 - 87
Frequency
8
12
8
8
8
5
9
8
(i)
19
(ii)
16
(iii)
14
(iv)
18
(v)
17
Question
2
2.
The following cumulative frequency table represents which of the following frequency distribution
Class-Interval
Cumulative Frequency
28 - 37
78
37 - 46
66
46 - 55
61
55 - 64
45
64 - 73
37
73 - 82
26
82 - 91
14
91 - 100
6
(i)
Class-Interval
28 - 37
37 - 46
46 - 55
55 - 64
64 - 73
73 - 82
82 - 91
91 - 100
Frequency
12
5
11
8
11
12
8
6
(ii)
Class-Interval
28 - 37
37 - 46
46 - 55
55 - 64
64 - 73
73 - 82
82 - 91
91 - 100
Frequency
12
5
16
8
13
12
8
6
(iii)
Class-Interval
28 - 37
37 - 46
46 - 55
55 - 64
64 - 73
73 - 82
82 - 91
91 - 100
Frequency
12
6
16
8
11
12
8
5
(iv)
Class-Interval
28 - 37
37 - 46
46 - 55
55 - 64
64 - 73
73 - 82
82 - 91
91 - 100
Frequency
12
5
16
8
11
12
8
6
(v)
Class-Interval
28 - 37
37 - 46
46 - 55
55 - 64
64 - 73
73 - 82
82 - 91
91 - 100
Frequency
12
5
8
16
11
12
8
6
Question
3
3.
The mid value of the class with frequency x is
Class-Interval
Frequency
14 - 19
28
19 - 24
9
24 - 29
x
29 - 34
5
34 - 39
7
(i)
105
4
(ii)
55
2
(iii)
53
2
(iv)
27
(v)
51
2
Question
4
4.
The true lower limit and true upper limit of the class with frequency x is
Class-Interval
Frequency
19 - 24
10
25 - 30
x
31 - 36
22
37 - 42
23
43 - 48
21
(i)
24
-
30.5
(ii)
24
-
31
(iii)
24.5
-
30.5
(iv)
24.5
-
31
(v)
25
-
30
Question
5
5.
The class boundaries of 13 - 20 which is in exclusive form are
(i)
12.5
-
20
(ii)
13
-
20.5
(iii)
12.5
-
20.5
(iv)
13.5
-
19.5
(v)
13
-
20
Question
6
6.
The class size used in the below table is
Class-Interval
34 - 43
43 - 52
52 - 61
61 - 70
70 - 79
79 - 88
88 - 97
97 - 106
Frequency
5
19
16
17
5
18
29
14
(i)
9
(ii)
11
(iii)
8
(iv)
7
(v)
10
Question
7
7.
If some random sample data is arranged in a frequency distribution table in
exclusive form
with
3
-
10
as the first class,
then the observation
25
falls in which class?
(i)
24.5
-
30.5
(ii)
23.5
-
31.5
(iii)
23
-
30
(iv)
25
-
32
(v)
24
-
31
Question
8
8.
Construct a frequency distribution table from the following cumulative frequency distribution
Class-Interval
Cumulative Frequency
24 - 30
13
30 - 36
24
36 - 42
34
42 - 48
46
48 - 54
61
54 - 60
76
60 - 66
90
(i)
Class-Interval
24 - 30
30 - 36
36 - 42
42 - 48
48 - 54
54 - 60
60 - 66
Frequency
13
11
10
7
15
15
14
(ii)
Class-Interval
24 - 30
30 - 36
36 - 42
42 - 48
48 - 54
54 - 60
60 - 66
Frequency
13
11
12
12
15
15
14
(iii)
Class-Interval
24 - 30
30 - 36
36 - 42
42 - 48
48 - 54
54 - 60
60 - 66
Frequency
13
10
11
12
15
15
14
(iv)
Class-Interval
24 - 30
30 - 36
36 - 42
42 - 48
48 - 54
54 - 60
60 - 66
Frequency
13
11
10
12
15
15
14
(v)
Class-Interval
24 - 30
30 - 36
36 - 42
42 - 48
48 - 54
54 - 60
60 - 66
Frequency
13
14
10
12
15
15
11
Question
9
9.
Find the cumulative frequency of class
70
-
77
.
Class-Interval
38 - 45
46 - 53
54 - 61
62 - 69
70 - 77
78 - 85
86 - 93
Frequency
21
6
6
7
13
22
12
(i)
54
(ii)
52
(iii)
51
(iv)
53
(v)
55
Question
10
10.
The true lower limit and true upper limit of the class with frequency x is
Class-Interval
Frequency
44 - 49
18
49 - 54
20
54 - 59
2
59 - 64
11
64 - 69
x
(i)
64.5
-
68.5
(ii)
63.5
-
69.5
(iii)
64
-
69.5
(iv)
64
-
69
(v)
63.5
-
69
Question
11
11.
If some random sample data is arranged in a frequency distribution table in
inclusive form
with
3
-
9
as the first class,
then the observation
23
falls in which class?
(i)
17.5
-
22.5
(ii)
17
-
23
(iii)
16.5
-
23.5
(iv)
16
-
22
(v)
18
-
24
Question
12
12.
The marks obtained by
18
students in an examination are given below.
Represent the data in the form of a frequency distribution table
in inclusive form
taking class size
6
.
53
59
75
50
64
55
79
59
57
52
75
43
60
65
42
57
57
58
(i)
Marks
42 - 47
48 - 53
54 - 59
60 - 65
66 - 71
72 - 77
78 - 83
No. of Students
2
3
7
8
0
2
1
(ii)
Marks
42 - 47
48 - 53
54 - 59
60 - 65
66 - 71
72 - 77
78 - 83
No. of Students
2
3
7
3
0
2
1
(iii)
Marks
42 - 47
48 - 53
54 - 59
60 - 65
66 - 71
72 - 77
78 - 83
No. of Students
2
3
4
3
0
2
1
(iv)
Marks
42 - 47
48 - 53
54 - 59
60 - 65
66 - 71
72 - 77
78 - 83
No. of Students
2
7
3
3
0
2
1
(v)
Marks
42 - 47
48 - 53
54 - 59
60 - 65
66 - 71
72 - 77
78 - 83
No. of Students
2
1
7
3
0
2
3
Question
13
13.
The daily wages (in rupees) of
15
workers in a factory are given below.
Represent the data in the form of a frequency distribution
in inclusive form
taking class size
20
.
230
272
200
246
294
216
262
245
287
224
279
289
239
257
239
(i)
Wages (in rupees)
200 - 219
220 - 239
240 - 259
260 - 279
280 - 299
No. of Workers
2
6
3
3
3
(ii)
Wages (in rupees)
200 - 219
220 - 239
240 - 259
260 - 279
280 - 299
No. of Workers
2
4
7
3
3
(iii)
Wages (in rupees)
200 - 219
220 - 239
240 - 259
260 - 279
280 - 299
No. of Workers
2
3
3
3
4
(iv)
Wages (in rupees)
200 - 219
220 - 239
240 - 259
260 - 279
280 - 299
No. of Workers
2
3
4
3
3
(v)
Wages (in rupees)
200 - 219
220 - 239
240 - 259
260 - 279
280 - 299
No. of Workers
2
4
3
3
3
Question
14
14.
Which of the following are discrete variables?
a)
Number of members in a family
b)
Wages of workers in a factory
c)
Weights of persons in a group
d)
Temperature at a place over a month
e)
Population of cities
(i)
{b,a}
(ii)
{c,e}
(iii)
{d,b,a}
(iv)
{a,e}
(v)
{c,e,a}
Question
15
15.
Following are the daily wages (in rupees) of labourers working in a factory. Identify the cumulative frequency of the given grouped data.
Wages (in rupees)
300 - 330
330 - 360
360 - 390
390 - 420
420 - 450
450 - 480
Labourers
9
16
7
17
18
9
(i)
Wages (in rupees)
Cumulative Frequency
300 - 330
9
330 - 360
25
360 - 390
34
390 - 420
51
420 - 450
69
450 - 480
78
(ii)
Wages (in rupees)
Cumulative Frequency
300 - 330
9
330 - 360
18
360 - 390
25
390 - 420
42
420 - 450
60
450 - 480
76
(iii)
Wages (in rupees)
Cumulative Frequency
300 - 330
9
330 - 360
16
360 - 390
32
390 - 420
49
420 - 450
67
450 - 480
76
(iv)
Wages (in rupees)
Cumulative Frequency
300 - 330
9
330 - 360
25
360 - 390
32
390 - 420
49
420 - 450
67
450 - 480
76
(v)
Wages (in rupees)
Cumulative Frequency
300 - 330
9
330 - 360
25
360 - 390
32
390 - 420
52
420 - 450
70
450 - 480
79
Question
16
16.
The class size used in the below table is
Class-Interval
25 - 31
32 - 38
39 - 45
46 - 52
53 - 59
60 - 66
Frequency
7
10
18
27
29
4
(i)
6
(ii)
8
(iii)
7
(iv)
9
(v)
4
Question
17
17.
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.
28
33
36
20
21
22
27
21
40
28
30
36
23
28
20
23
22
22
38
24
(i)
Size
20
21
22
23
24
27
28
30
33
36
38
40
No. of Shirts
2
2
3
2
1
1
3
1
1
2
1
1
(ii)
Size
20
21
23
24
28
29
31
32
33
34
35
36
37
38
39
No. of Shirts
1
1
1
1
1
2
1
2
1
2
1
1
1
1
3
(iii)
Size
20
21
22
23
24
28
30
33
36
38
40
No. of Shirts
2
2
3
2
1
3
2
1
2
1
1
(iv)
Size
22
25
26
27
30
31
33
34
35
37
38
39
40
No. of Shirts
1
3
1
1
2
2
1
2
1
2
2
1
1
Question
18
18.
Which of the following class intervals are in exclusive form?
a)
12.5 - 19.5 , 19.5 - 26.5 , 26.5 - 33.5...
b)
13 - 19 , 19 - 25 , 25 - 31,...
c)
13 - 19 , 20 - 26 , 27 - 33,...
d)
31 - 37 , 37 - 43 , 43 - 49...
e)
34 - 40 , 41 - 47 , 48 - 54,...
(i)
{c,a,b}
(ii)
{a,b,d}
(iii)
{c,a}
(iv)
{c,e,d}
(v)
{e,b}
Question
19
19.
The class mark of the class with frequency x is
Class-Interval
Frequency
20 - 30
24
30 - 40
x
40 - 50
2
50 - 60
24
60 - 70
15
(i)
34
(ii)
36
(iii)
33
(iv)
38
(v)
35
Question
20
20.
Given class interval
30
-
35
in exclusive form, its
class mark is
(i)
33
(ii)
67
2
(iii)
65
2
(iv)
129
4
(v)
63
2
Question
21
21.
In exclusive form representation, the observation
45
falls in which class?
(i)
50
-
60
(ii)
35
-
45
(iii)
55
-
65
(iv)
45
-
55
(v)
40
-
45
Question
22
22.
The upper limit of the class with frequency x is
Class-Interval
Frequency
11 - 21
10
21 - 31
23
31 - 41
19
41 - 51
x
51 - 61
25
(i)
50
(ii)
54
(iii)
52
(iv)
49
(v)
51
Question
23
23.
If the sum of the following frequency distribution is
29
,
find the value of 'x'.
Class-Interval
Frequency
20 - 29
9
30 - 39
6
40 - 49
4
50 - 59
2
60 - 69
x
70 - 79
7
(i)
1
(ii)
-2
(iii)
3
(iv)
2
(v)
0
Question
24
24.
Convert the continuous form of the class interval 46.5 - 49.5 to discontinuous form
(i)
47
-
49
(ii)
47
-
49.5
(iii)
47.5
-
48.5
(iv)
46.5
-
49.5
(v)
46.5
-
49
Question
25
25.
If the sample data with range 60 has to be divided into 6 class intervals, then the length of the class is
(i)
9
(ii)
11
(iii)
12
(iv)
8
(v)
10
Assignment Key
1) (v)
2) (iv)
3) (iii)
4) (iii)
5) (v)
6) (i)
7) (v)
8) (iv)
9) (iv)
10) (iv)
11) (ii)
12) (ii)
13) (v)
14) (iv)
15) (iv)
16) (iii)
17) (i)
18) (ii)
19) (v)
20) (iii)
21) (iv)
22) (v)
23) (i)
24) (i)
25) (v)
