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
11 - 21
11
22 - 32
21
33 - 43
28
44 - 54
36
55 - 65
52
(i)
Class-Interval
11 - 21
22 - 32
33 - 43
44 - 54
55 - 65
Frequency
11
7
10
8
16
(ii)
Class-Interval
11 - 21
22 - 32
33 - 43
44 - 54
55 - 65
Frequency
11
8
7
8
16
(iii)
Class-Interval
11 - 21
22 - 32
33 - 43
44 - 54
55 - 65
Frequency
11
10
11
8
16
(iv)
Class-Interval
11 - 21
22 - 32
33 - 43
44 - 54
55 - 65
Frequency
11
16
7
8
10
(v)
Class-Interval
11 - 21
22 - 32
33 - 43
44 - 54
55 - 65
Frequency
11
10
7
8
16
Question
2
2.
Construct a frequency distribution table from the following cumulative frequency distribution
Class-Interval
Cumulative Frequency
34 - 41
15
41 - 48
28
48 - 55
39
55 - 62
44
62 - 69
54
69 - 76
66
76 - 83
73
(i)
Class-Interval
34 - 41
41 - 48
48 - 55
55 - 62
62 - 69
69 - 76
76 - 83
Frequency
15
13
11
5
10
12
7
(ii)
Class-Interval
34 - 41
41 - 48
48 - 55
55 - 62
62 - 69
69 - 76
76 - 83
Frequency
15
11
13
5
10
12
7
(iii)
Class-Interval
34 - 41
41 - 48
48 - 55
55 - 62
62 - 69
69 - 76
76 - 83
Frequency
15
13
11
2
10
12
7
(iv)
Class-Interval
34 - 41
41 - 48
48 - 55
55 - 62
62 - 69
69 - 76
76 - 83
Frequency
15
13
9
5
10
12
7
(v)
Class-Interval
34 - 41
41 - 48
48 - 55
55 - 62
62 - 69
69 - 76
76 - 83
Frequency
15
7
11
5
10
12
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
64 - 74
75 - 85
No. of Patients
33
81
32
14
54
79
(i)
Age (in years)
Cumulative Frequency
20 - 30
33
31 - 41
112
42 - 52
144
53 - 63
158
64 - 74
212
75 - 85
293
(ii)
Age (in years)
Cumulative Frequency
20 - 30
33
31 - 41
65
42 - 52
146
53 - 63
160
64 - 74
214
75 - 85
293
(iii)
Age (in years)
Cumulative Frequency
20 - 30
33
31 - 41
114
42 - 52
146
53 - 63
160
64 - 74
214
75 - 85
293
(iv)
Age (in years)
Cumulative Frequency
20 - 30
33
31 - 41
114
42 - 52
146
53 - 63
164
64 - 74
218
75 - 85
297
(v)
Age (in years)
Cumulative Frequency
20 - 30
33
31 - 41
114
42 - 52
149
53 - 63
163
64 - 74
217
75 - 85
296
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)
10 - 15
15 - 20
20 - 25
25 - 30
No. of Patients
21
62
21
35
(i)
Age (in years)
Cumulative Frequency
10 - 15
21
15 - 20
83
20 - 25
107
25 - 30
142
(ii)
Age (in years)
Cumulative Frequency
10 - 15
21
15 - 20
86
20 - 25
107
25 - 30
142
(iii)
Age (in years)
Cumulative Frequency
10 - 15
35
15 - 20
97
20 - 25
118
25 - 30
139
(iv)
Age (in years)
Cumulative Frequency
10 - 15
21
15 - 20
83
20 - 25
104
25 - 30
139
(v)
Age (in years)
Cumulative Frequency
10 - 15
21
15 - 20
42
20 - 25
104
25 - 30
139
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 - 320
321 - 341
342 - 362
363 - 383
384 - 404
405 - 425
Labourers
5
5
20
12
5
6
(i)
Wages (in rupees)
Cumulative Frequency
300 - 320
5
321 - 341
11
342 - 362
31
363 - 383
43
384 - 404
48
405 - 425
53
(ii)
Wages (in rupees)
Cumulative Frequency
300 - 320
5
321 - 341
10
342 - 362
30
363 - 383
39
384 - 404
44
405 - 425
50
(iii)
Wages (in rupees)
Cumulative Frequency
300 - 320
5
321 - 341
25
342 - 362
30
363 - 383
42
384 - 404
47
405 - 425
53
(iv)
Wages (in rupees)
Cumulative Frequency
300 - 320
5
321 - 341
10
342 - 362
30
363 - 383
42
384 - 404
47
405 - 425
53
(v)
Wages (in rupees)
Cumulative Frequency
300 - 320
5
321 - 341
10
342 - 362
32
363 - 383
44
384 - 404
49
405 - 425
55
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 - 320
320 - 340
340 - 360
360 - 380
380 - 400
400 - 420
Labourers
7
5
4
4
19
19
(i)
Wages (in rupees)
Cumulative Frequency
300 - 320
7
320 - 340
12
340 - 360
16
360 - 380
20
380 - 400
39
400 - 420
58
(ii)
Wages (in rupees)
Cumulative Frequency
300 - 320
7
320 - 340
12
340 - 360
14
360 - 380
18
380 - 400
37
400 - 420
56
(iii)
Wages (in rupees)
Cumulative Frequency
300 - 320
7
320 - 340
12
340 - 360
16
360 - 380
17
380 - 400
36
400 - 420
55
(iv)
Wages (in rupees)
Cumulative Frequency
300 - 320
7
320 - 340
26
340 - 360
30
360 - 380
34
380 - 400
53
400 - 420
58
(v)
Wages (in rupees)
Cumulative Frequency
300 - 320
7
320 - 340
11
340 - 360
16
360 - 380
20
380 - 400
39
400 - 420
58
Question
7
7.
Identify the cumulative frequency of the given grouped data.
class interval
42 - 47
48 - 53
54 - 59
60 - 65
66 - 71
frequency
18
22
14
21
9
(i)
class interval
Cumulative Frequency
42 - 47
18
48 - 53
32
54 - 59
54
60 - 65
75
66 - 71
84
(ii)
class interval
Cumulative Frequency
42 - 47
18
48 - 53
40
54 - 59
54
60 - 65
75
66 - 71
84
(iii)
class interval
Cumulative Frequency
42 - 47
18
48 - 53
40
54 - 59
49
60 - 65
70
66 - 71
79
(iv)
class interval
Cumulative Frequency
42 - 47
18
48 - 53
27
54 - 59
41
60 - 65
62
66 - 71
84
(v)
class interval
Cumulative Frequency
42 - 47
18
48 - 53
35
54 - 59
49
60 - 65
70
66 - 71
79
Question
8
8.
Identify the cumulative frequency of the given grouped data.
class interval
48 - 56
56 - 64
64 - 72
72 - 80
80 - 88
frequency
11
24
14
16
23
(i)
class interval
Cumulative Frequency
48 - 56
11
56 - 64
34
64 - 72
48
72 - 80
64
80 - 88
88
(ii)
class interval
Cumulative Frequency
48 - 56
11
56 - 64
35
64 - 72
49
72 - 80
65
80 - 88
88
(iii)
class interval
Cumulative Frequency
48 - 56
11
56 - 64
25
64 - 72
49
72 - 80
65
80 - 88
88
(iv)
class interval
Cumulative Frequency
48 - 56
11
56 - 64
35
64 - 72
44
72 - 80
60
80 - 88
83
(v)
class interval
Cumulative Frequency
48 - 56
11
56 - 64
40
64 - 72
54
72 - 80
70
80 - 88
93
Question
9
9.
Less than cumulative curves are drawn using
(i)
lower boundaries of classes and less than cumulative frequencies
(ii)
lower boundaries of classes and greater than cumulative frequencies
(iii)
mid values of classes and less than cumulative frequencies
(iv)
upper boundaries of classes and less than cumulative frequencies
Question
10
10.
Greater than cumulative curves are drawn using
(i)
upper boundaries of classes and less than cumulative frequencies
(ii)
upper boundaries of classes and greater than cumulative frequencies
(iii)
lower boundaries of classes and greater than cumulative frequencies
(iv)
mid values of classes and greater than cumulative frequencies
Question
11
11.
Find the cumulative frequency of class
47
-
54
.
Class-Interval
15 - 22
23 - 30
31 - 38
39 - 46
47 - 54
55 - 62
63 - 70
Frequency
23
14
7
18
25
23
5
(i)
85
(ii)
90
(iii)
88
(iv)
87
(v)
86
Question
12
12.
Find the cumulative frequency of class
89
-
96
.
Class-Interval
40 - 47
47 - 54
54 - 61
61 - 68
68 - 75
75 - 82
82 - 89
89 - 96
Frequency
6
5
7
11
8
21
15
14
(i)
86
(ii)
88
(iii)
87
(iv)
84
(v)
89
Question
13
13.
The following cumulative frequency table represents which of the following frequency distribution
Class-Interval
Cumulative Frequency
39 - 48
15
48 - 57
22
57 - 66
38
66 - 75
54
75 - 84
65
84 - 93
75
93 - 102
85
102 - 111
92
(i)
Class-Interval
39 - 48
48 - 57
57 - 66
66 - 75
75 - 84
84 - 93
93 - 102
102 - 111
Frequency
15
7
11
16
11
10
10
7
(ii)
Class-Interval
39 - 48
48 - 57
57 - 66
66 - 75
75 - 84
84 - 93
93 - 102
102 - 111
Frequency
15
7
16
16
11
10
10
7
(iii)
Class-Interval
39 - 48
48 - 57
57 - 66
66 - 75
75 - 84
84 - 93
93 - 102
102 - 111
Frequency
15
7
16
16
14
10
10
7
Question
14
14.
The following cumulative frequency table represents which of the following frequency distribution
Class-Interval
Cumulative Frequency
14 - 19
61
19 - 24
52
24 - 29
41
29 - 34
36
34 - 39
21
39 - 44
8
(i)
Class-Interval
14 - 19
19 - 24
24 - 29
29 - 34
34 - 39
39 - 44
Frequency
9
11
10
15
13
8
(ii)
Class-Interval
14 - 19
19 - 24
24 - 29
29 - 34
34 - 39
39 - 44
Frequency
9
8
5
15
13
11
(iii)
Class-Interval
14 - 19
19 - 24
24 - 29
29 - 34
34 - 39
39 - 44
Frequency
9
11
5
10
13
8
(iv)
Class-Interval
14 - 19
19 - 24
24 - 29
29 - 34
34 - 39
39 - 44
Frequency
9
5
11
15
13
8
(v)
Class-Interval
14 - 19
19 - 24
24 - 29
29 - 34
34 - 39
39 - 44
Frequency
9
11
5
15
13
8
Question
15
15.
During the medical check-up of 60 students of a class, their weights in kgs are recorded as follows.
Identify the number of students whose weight is more than 76 kg
Class-Interval
31 - 40
40 - 49
49 - 58
58 - 67
67 - 76
76 - 85
85 - 94
Frequency
9
5
8
11
7
11
9
(i)
20
(ii)
23
(iii)
21
(iv)
19
(v)
17
Assignment Key
1) (v)
2) (i)
3) (iii)
4) (iv)
5) (iv)
6) (i)
7) (ii)
8) (ii)
9) (iv)
10) (iii)
11) (iv)
12) (iii)
13) (ii)
14) (v)
15) (i)
