EduSahara™ Assignment
Name : Cumulative Frequency Distribution
Chapter : Statistics
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
Construct a frequency distribution table from the following cumulative frequency distribution
Class-Interval
Cumulative Frequency
32 - 39
16
40 - 47
26
48 - 55
34
56 - 63
45
64 - 71
50
72 - 79
60
(i)
Class-Interval
32 - 39
40 - 47
48 - 55
56 - 63
64 - 71
72 - 79
Frequency
16
8
10
11
5
10
(ii)
Class-Interval
32 - 39
40 - 47
48 - 55
56 - 63
64 - 71
72 - 79
Frequency
16
10
4
11
5
10
(iii)
Class-Interval
32 - 39
40 - 47
48 - 55
56 - 63
64 - 71
72 - 79
Frequency
16
10
8
11
5
10
(iv)
Class-Interval
32 - 39
40 - 47
48 - 55
56 - 63
64 - 71
72 - 79
Frequency
16
10
8
9
5
10
Question
2
2.
Construct a frequency distribution table from the following cumulative frequency distribution
Class-Interval
Cumulative Frequency
15 - 24
14
24 - 33
27
33 - 42
43
42 - 51
48
51 - 60
55
(i)
Class-Interval
15 - 24
24 - 33
33 - 42
42 - 51
51 - 60
Frequency
14
16
16
5
7
(ii)
Class-Interval
15 - 24
24 - 33
33 - 42
42 - 51
51 - 60
Frequency
14
13
16
5
7
(iii)
Class-Interval
15 - 24
24 - 33
33 - 42
42 - 51
51 - 60
Frequency
14
16
13
5
7
(iv)
Class-Interval
15 - 24
24 - 33
33 - 42
42 - 51
51 - 60
Frequency
14
13
12
5
7
(v)
Class-Interval
15 - 24
24 - 33
33 - 42
42 - 51
51 - 60
Frequency
14
7
16
5
13
Question
3
3.
Following are the ages (in years) of patients getting medical treatment in a hospital. Identify the cumulative frequency of the given grouped data.
Age (in years)
20 - 30
31 - 41
42 - 52
53 - 63
No. of Patients
48
52
70
41
(i)
Age (in years)
Cumulative Frequency
20 - 30
48
31 - 41
100
42 - 52
165
53 - 63
206
(ii)
Age (in years)
Cumulative Frequency
20 - 30
48
31 - 41
100
42 - 52
170
53 - 63
211
(iii)
Age (in years)
Cumulative Frequency
20 - 30
48
31 - 41
103
42 - 52
173
53 - 63
214
(iv)
Age (in years)
Cumulative Frequency
20 - 30
48
31 - 41
118
42 - 52
170
53 - 63
211
(v)
Age (in years)
Cumulative Frequency
20 - 30
41
31 - 41
93
42 - 52
163
53 - 63
211
Question
4
4.
Following are the ages (in years) of patients getting medical treatment in a hospital. Identify the cumulative frequency of the given grouped data.
Age (in years)
20 - 30
30 - 40
40 - 50
50 - 60
60 - 70
No. of Patients
38
71
73
18
63
(i)
Age (in years)
Cumulative Frequency
20 - 30
38
30 - 40
109
40 - 50
185
50 - 60
203
60 - 70
266
(ii)
Age (in years)
Cumulative Frequency
20 - 30
38
30 - 40
111
40 - 50
182
50 - 60
200
60 - 70
263
(iii)
Age (in years)
Cumulative Frequency
20 - 30
38
30 - 40
112
40 - 50
185
50 - 60
203
60 - 70
266
(iv)
Age (in years)
Cumulative Frequency
20 - 30
38
30 - 40
101
40 - 50
174
50 - 60
192
60 - 70
263
(v)
Age (in years)
Cumulative Frequency
20 - 30
38
30 - 40
109
40 - 50
182
50 - 60
200
60 - 70
263
Question
5
5.
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 - 340
341 - 381
382 - 422
423 - 463
464 - 504
505 - 545
Labourers
10
5
8
17
13
3
(i)
Wages (in rupees)
Cumulative Frequency
300 - 340
10
341 - 381
15
382 - 422
23
423 - 463
45
464 - 504
58
505 - 545
61
(ii)
Wages (in rupees)
Cumulative Frequency
300 - 340
10
341 - 381
18
382 - 422
23
423 - 463
40
464 - 504
53
505 - 545
56
(iii)
Wages (in rupees)
Cumulative Frequency
300 - 340
10
341 - 381
15
382 - 422
27
423 - 463
44
464 - 504
57
505 - 545
60
(iv)
Wages (in rupees)
Cumulative Frequency
300 - 340
10
341 - 381
13
382 - 422
21
423 - 463
38
464 - 504
51
505 - 545
56
(v)
Wages (in rupees)
Cumulative Frequency
300 - 340
10
341 - 381
15
382 - 422
23
423 - 463
40
464 - 504
53
505 - 545
56
Question
6
6.
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
12
13
18
11
6
18
(i)
Wages (in rupees)
Cumulative Frequency
300 - 330
12
330 - 360
25
360 - 390
43
390 - 420
54
420 - 450
60
450 - 480
78
(ii)
Wages (in rupees)
Cumulative Frequency
300 - 330
12
330 - 360
30
360 - 390
48
390 - 420
59
420 - 450
65
450 - 480
78
(iii)
Wages (in rupees)
Cumulative Frequency
300 - 330
12
330 - 360
25
360 - 390
43
390 - 420
52
420 - 450
58
450 - 480
76
(iv)
Wages (in rupees)
Cumulative Frequency
300 - 330
12
330 - 360
25
360 - 390
48
390 - 420
59
420 - 450
65
450 - 480
83
(v)
Wages (in rupees)
Cumulative Frequency
300 - 330
12
330 - 360
30
360 - 390
43
390 - 420
54
420 - 450
60
450 - 480
78
Question
7
7.
Identify the cumulative frequency of the given grouped data.
class interval
40 - 50
51 - 61
62 - 72
73 - 83
84 - 94
95 - 105
106 - 116
117 - 127
frequency
22
9
16
19
9
21
18
16
(i)
class interval
Cumulative Frequency
40 - 50
22
51 - 61
31
62 - 72
47
73 - 83
66
84 - 94
75
95 - 105
96
106 - 116
114
117 - 127
130
(ii)
class interval
Cumulative Frequency
40 - 50
22
51 - 61
31
62 - 72
50
73 - 83
66
84 - 94
75
95 - 105
96
106 - 116
114
117 - 127
130
(iii)
class interval
Cumulative Frequency
40 - 50
22
51 - 61
31
62 - 72
49
73 - 83
68
84 - 94
77
95 - 105
98
106 - 116
116
117 - 127
132
(iv)
class interval
Cumulative Frequency
40 - 50
22
51 - 61
31
62 - 72
47
73 - 83
66
84 - 94
77
95 - 105
98
106 - 116
116
117 - 127
132
(v)
class interval
Cumulative Frequency
40 - 50
22
51 - 61
38
62 - 72
54
73 - 83
73
84 - 94
82
95 - 105
103
106 - 116
121
117 - 127
130
Question
8
8.
Identify the cumulative frequency of the given grouped data.
class interval
20 - 26
26 - 32
32 - 38
38 - 44
44 - 50
50 - 56
frequency
20
24
23
18
8
21
(i)
class interval
Cumulative Frequency
20 - 26
20
26 - 32
41
32 - 38
64
38 - 44
82
44 - 50
90
50 - 56
114
(ii)
class interval
Cumulative Frequency
20 - 26
20
26 - 32
44
32 - 38
72
38 - 44
90
44 - 50
98
50 - 56
119
(iii)
class interval
Cumulative Frequency
20 - 26
20
26 - 32
44
32 - 38
67
38 - 44
85
44 - 50
93
50 - 56
114
(iv)
class interval
Cumulative Frequency
20 - 26
20
26 - 32
44
32 - 38
67
38 - 44
81
44 - 50
89
50 - 56
110
(v)
class interval
Cumulative Frequency
20 - 26
20
26 - 32
43
32 - 38
67
38 - 44
85
44 - 50
93
50 - 56
114
Question
9
9.
Less than cumulative curves are drawn using
(i)
mid values of classes and less than cumulative frequencies
(ii)
lower boundaries of classes and greater than cumulative frequencies
(iii)
upper boundaries of classes and less than cumulative frequencies
(iv)
lower boundaries of classes and less than cumulative frequencies
Question
10
10.
Greater than cumulative curves are drawn using
(i)
upper boundaries of classes and greater than cumulative frequencies
(ii)
lower boundaries of classes and greater than cumulative frequencies
(iii)
upper boundaries of classes and less than cumulative frequencies
(iv)
mid values of classes and greater than cumulative frequencies
Question
11
11.
Find the cumulative frequency of class
43
-
51
.
Class-Interval
16 - 24
25 - 33
34 - 42
43 - 51
Frequency
6
7
23
20
(i)
59
(ii)
55
(iii)
56
(iv)
57
(v)
54
Question
12
12.
Find the cumulative frequency of class
87
-
97
.
Class-Interval
37 - 47
47 - 57
57 - 67
67 - 77
77 - 87
87 - 97
97 - 107
107 - 117
Frequency
13
25
14
8
11
7
20
12
(i)
79
(ii)
78
(iii)
76
(iv)
81
(v)
77
Question
13
13.
The following cumulative frequency table represents which of the following frequency distribution
Class-Interval
Cumulative Frequency
15 - 24
5
24 - 33
10
33 - 42
18
42 - 51
26
51 - 60
31
(i)
Class-Interval
15 - 24
24 - 33
33 - 42
42 - 51
51 - 60
Frequency
5
5
8
8
5
(ii)
Class-Interval
15 - 24
24 - 33
33 - 42
42 - 51
51 - 60
Frequency
5
5
3
8
5
(iii)
Class-Interval
15 - 24
24 - 33
33 - 42
42 - 51
51 - 60
Frequency
5
3
8
8
5
(iv)
Class-Interval
15 - 24
24 - 33
33 - 42
42 - 51
51 - 60
Frequency
5
8
5
8
5
Question
14
14.
The following cumulative frequency table represents which of the following frequency distribution
Class-Interval
Cumulative Frequency
24 - 31
85
31 - 38
72
38 - 45
66
45 - 52
51
52 - 59
45
59 - 66
32
66 - 73
16
73 - 80
10
(i)
Class-Interval
24 - 31
31 - 38
38 - 45
45 - 52
52 - 59
59 - 66
66 - 73
73 - 80
Frequency
13
6
11
6
13
16
6
10
(ii)
Class-Interval
24 - 31
31 - 38
38 - 45
45 - 52
52 - 59
59 - 66
66 - 73
73 - 80
Frequency
13
10
15
6
13
16
6
6
(iii)
Class-Interval
24 - 31
31 - 38
38 - 45
45 - 52
52 - 59
59 - 66
66 - 73
73 - 80
Frequency
13
6
15
6
18
16
6
10
(iv)
Class-Interval
24 - 31
31 - 38
38 - 45
45 - 52
52 - 59
59 - 66
66 - 73
73 - 80
Frequency
13
6
6
15
13
16
6
10
(v)
Class-Interval
24 - 31
31 - 38
38 - 45
45 - 52
52 - 59
59 - 66
66 - 73
73 - 80
Frequency
13
6
15
6
13
16
6
10
Question
15
15.
During the medical check-up of 69 students of a class, their weights in kgs are recorded as follows.
Identify the number of students whose weight is more than 39 kg
Class-Interval
30 - 39
39 - 48
48 - 57
57 - 66
66 - 75
75 - 84
84 - 93
93 - 102
Frequency
11
10
8
9
9
8
9
5
(i)
57
(ii)
58
(iii)
56
(iv)
59
(v)
61
Assignment Key
1) (iii)
2) (ii)
3) (ii)
4) (v)
5) (v)
6) (i)
7) (i)
8) (iii)
9) (iii)
10) (ii)
11) (iii)
12) (ii)
13) (i)
14) (v)
15) (ii)
