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
18 - 25
6
26 - 33
12
34 - 41
25
42 - 49
35
50 - 57
41
58 - 65
49
66 - 73
62
(i)
Class-Interval
18 - 25
26 - 33
34 - 41
42 - 49
50 - 57
58 - 65
66 - 73
Frequency
6
6
13
15
6
8
13
(ii)
Class-Interval
18 - 25
26 - 33
34 - 41
42 - 49
50 - 57
58 - 65
66 - 73
Frequency
6
6
13
10
6
8
13
(iii)
Class-Interval
18 - 25
26 - 33
34 - 41
42 - 49
50 - 57
58 - 65
66 - 73
Frequency
6
6
18
10
6
8
13
(iv)
Class-Interval
18 - 25
26 - 33
34 - 41
42 - 49
50 - 57
58 - 65
66 - 73
Frequency
6
13
6
10
6
8
13
(v)
Class-Interval
18 - 25
26 - 33
34 - 41
42 - 49
50 - 57
58 - 65
66 - 73
Frequency
6
13
13
10
6
8
6
Question
2
2.
Construct a frequency distribution table from the following cumulative frequency distribution
Class-Interval
Cumulative Frequency
24 - 34
8
34 - 44
18
44 - 54
27
54 - 64
43
64 - 74
54
74 - 84
66
(i)
Class-Interval
24 - 34
34 - 44
44 - 54
54 - 64
64 - 74
74 - 84
Frequency
8
10
9
14
11
12
(ii)
Class-Interval
24 - 34
34 - 44
44 - 54
54 - 64
64 - 74
74 - 84
Frequency
8
10
9
16
11
12
(iii)
Class-Interval
24 - 34
34 - 44
44 - 54
54 - 64
64 - 74
74 - 84
Frequency
8
9
10
16
11
12
(iv)
Class-Interval
24 - 34
34 - 44
44 - 54
54 - 64
64 - 74
74 - 84
Frequency
8
12
9
16
11
10
(v)
Class-Interval
24 - 34
34 - 44
44 - 54
54 - 64
64 - 74
74 - 84
Frequency
8
10
11
16
11
12
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 - 25
26 - 31
32 - 37
38 - 43
44 - 49
50 - 55
56 - 61
62 - 67
No. of Patients
53
48
86
85
47
35
16
16
(i)
Age (in years)
Cumulative Frequency
20 - 25
53
26 - 31
69
32 - 37
155
38 - 43
240
44 - 49
287
50 - 55
322
56 - 61
338
62 - 67
386
(ii)
Age (in years)
Cumulative Frequency
20 - 25
53
26 - 31
101
32 - 37
190
38 - 43
275
44 - 49
322
50 - 55
357
56 - 61
373
62 - 67
389
(iii)
Age (in years)
Cumulative Frequency
20 - 25
53
26 - 31
101
32 - 37
187
38 - 43
272
44 - 49
324
50 - 55
359
56 - 61
375
62 - 67
391
(iv)
Age (in years)
Cumulative Frequency
20 - 25
53
26 - 31
101
32 - 37
186
38 - 43
272
44 - 49
319
50 - 55
354
56 - 61
370
62 - 67
386
(v)
Age (in years)
Cumulative Frequency
20 - 25
53
26 - 31
101
32 - 37
187
38 - 43
272
44 - 49
319
50 - 55
354
56 - 61
370
62 - 67
386
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
63
17
39
14
(i)
Age (in years)
Cumulative Frequency
10 - 15
63
15 - 20
80
20 - 25
123
25 - 30
137
(ii)
Age (in years)
Cumulative Frequency
10 - 15
14
15 - 20
31
20 - 25
70
25 - 30
133
(iii)
Age (in years)
Cumulative Frequency
10 - 15
63
15 - 20
102
20 - 25
119
25 - 30
133
(iv)
Age (in years)
Cumulative Frequency
10 - 15
63
15 - 20
80
20 - 25
119
25 - 30
133
(v)
Age (in years)
Cumulative Frequency
10 - 15
63
15 - 20
83
20 - 25
122
25 - 30
136
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
9
14
18
8
9
18
(i)
Wages (in rupees)
Cumulative Frequency
300 - 340
9
341 - 381
23
382 - 422
41
423 - 463
44
464 - 504
53
505 - 545
71
(ii)
Wages (in rupees)
Cumulative Frequency
300 - 340
9
341 - 381
23
382 - 422
43
423 - 463
51
464 - 504
60
505 - 545
78
(iii)
Wages (in rupees)
Cumulative Frequency
300 - 340
9
341 - 381
27
382 - 422
45
423 - 463
53
464 - 504
62
505 - 545
76
(iv)
Wages (in rupees)
Cumulative Frequency
300 - 340
9
341 - 381
23
382 - 422
41
423 - 463
49
464 - 504
58
505 - 545
76
(v)
Wages (in rupees)
Cumulative Frequency
300 - 340
9
341 - 381
27
382 - 422
41
423 - 463
49
464 - 504
58
505 - 545
76
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)
200 - 220
220 - 240
240 - 260
260 - 280
280 - 300
300 - 320
Labourers
19
1
9
18
16
15
(i)
Wages (in rupees)
Cumulative Frequency
200 - 220
19
220 - 240
20
240 - 260
33
260 - 280
51
280 - 300
67
300 - 320
82
(ii)
Wages (in rupees)
Cumulative Frequency
200 - 220
19
220 - 240
28
240 - 260
29
260 - 280
47
280 - 300
63
300 - 320
78
(iii)
Wages (in rupees)
Cumulative Frequency
200 - 220
19
220 - 240
20
240 - 260
29
260 - 280
47
280 - 300
63
300 - 320
78
(iv)
Wages (in rupees)
Cumulative Frequency
200 - 220
19
220 - 240
20
240 - 260
29
260 - 280
45
280 - 300
61
300 - 320
76
(v)
Wages (in rupees)
Cumulative Frequency
200 - 220
19
220 - 240
34
240 - 260
43
260 - 280
61
280 - 300
77
300 - 320
78
Question
7
7.
Identify the cumulative frequency of the given grouped data.
class interval
23 - 28
29 - 34
35 - 40
41 - 46
47 - 52
53 - 58
59 - 64
frequency
12
14
24
8
13
17
7
(i)
class interval
Cumulative Frequency
23 - 28
12
29 - 34
26
35 - 40
50
41 - 46
58
47 - 52
71
53 - 58
88
59 - 64
95
(ii)
class interval
Cumulative Frequency
23 - 28
12
29 - 34
19
35 - 40
43
41 - 46
51
47 - 52
64
53 - 58
81
59 - 64
95
(iii)
class interval
Cumulative Frequency
23 - 28
12
29 - 34
26
35 - 40
52
41 - 46
60
47 - 52
73
53 - 58
90
59 - 64
97
(iv)
class interval
Cumulative Frequency
23 - 28
12
29 - 34
26
35 - 40
50
41 - 46
63
47 - 52
76
53 - 58
93
59 - 64
100
(v)
class interval
Cumulative Frequency
23 - 28
12
29 - 34
36
35 - 40
50
41 - 46
58
47 - 52
71
53 - 58
88
59 - 64
95
Question
8
8.
Identify the cumulative frequency of the given grouped data.
class interval
42 - 51
51 - 60
60 - 69
69 - 78
78 - 87
87 - 96
96 - 105
frequency
8
20
11
9
13
24
12
(i)
class interval
Cumulative Frequency
42 - 51
8
51 - 60
20
60 - 69
31
69 - 78
40
78 - 87
53
87 - 96
77
96 - 105
97
(ii)
class interval
Cumulative Frequency
42 - 51
8
51 - 60
19
60 - 69
39
69 - 78
48
78 - 87
61
87 - 96
85
96 - 105
97
(iii)
class interval
Cumulative Frequency
42 - 51
8
51 - 60
28
60 - 69
39
69 - 78
48
78 - 87
61
87 - 96
85
96 - 105
97
(iv)
class interval
Cumulative Frequency
42 - 51
8
51 - 60
28
60 - 69
34
69 - 78
43
78 - 87
56
87 - 96
80
96 - 105
92
(v)
class interval
Cumulative Frequency
42 - 51
8
51 - 60
28
60 - 69
39
69 - 78
50
78 - 87
63
87 - 96
87
96 - 105
99
Question
9
9.
Less than cumulative curves are drawn using
(i)
lower boundaries of classes and greater than cumulative frequencies
(ii)
upper boundaries of classes and less than cumulative frequencies
(iii)
lower boundaries of classes and less than cumulative frequencies
(iv)
mid values 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)
upper boundaries of classes and less than cumulative frequencies
(iii)
mid values of classes and greater than cumulative frequencies
(iv)
lower boundaries of classes and greater than cumulative frequencies
Question
11
11.
Find the cumulative frequency of class
60
-
65
.
Class-Interval
36 - 41
42 - 47
48 - 53
54 - 59
60 - 65
Frequency
14
17
17
18
25
(i)
88
(ii)
92
(iii)
91
(iv)
94
(v)
90
Question
12
12.
Find the cumulative frequency of class
22
-
28
.
Class-Interval
16 - 22
22 - 28
28 - 34
34 - 40
40 - 46
46 - 52
52 - 58
Frequency
6
7
11
15
10
17
8
(i)
13
(ii)
10
(iii)
15
(iv)
12
(v)
14
Question
13
13.
The following cumulative frequency table represents which of the following frequency distribution
Class-Interval
Cumulative Frequency
13 - 21
5
21 - 29
10
29 - 37
24
37 - 45
29
45 - 53
41
53 - 61
52
(i)
Class-Interval
13 - 21
21 - 29
29 - 37
37 - 45
45 - 53
53 - 61
Frequency
5
14
5
5
12
11
(ii)
Class-Interval
13 - 21
21 - 29
29 - 37
37 - 45
45 - 53
53 - 61
Frequency
5
11
14
5
12
5
(iii)
Class-Interval
13 - 21
21 - 29
29 - 37
37 - 45
45 - 53
53 - 61
Frequency
5
5
14
10
12
11
(iv)
Class-Interval
13 - 21
21 - 29
29 - 37
37 - 45
45 - 53
53 - 61
Frequency
5
5
18
5
12
11
(v)
Class-Interval
13 - 21
21 - 29
29 - 37
37 - 45
45 - 53
53 - 61
Frequency
5
5
14
5
12
11
Question
14
14.
The following cumulative frequency table represents which of the following frequency distribution
Class-Interval
Cumulative Frequency
28 - 38
73
38 - 48
65
48 - 58
56
58 - 68
49
68 - 78
37
78 - 88
24
88 - 98
18
98 - 108
13
(i)
Class-Interval
28 - 38
38 - 48
48 - 58
58 - 68
68 - 78
78 - 88
88 - 98
98 - 108
Frequency
8
9
12
7
13
6
5
13
(ii)
Class-Interval
28 - 38
38 - 48
48 - 58
58 - 68
68 - 78
78 - 88
88 - 98
98 - 108
Frequency
8
13
7
12
13
6
5
9
(iii)
Class-Interval
28 - 38
38 - 48
48 - 58
58 - 68
68 - 78
78 - 88
88 - 98
98 - 108
Frequency
8
9
7
12
13
6
5
13
(iv)
Class-Interval
28 - 38
38 - 48
48 - 58
58 - 68
68 - 78
78 - 88
88 - 98
98 - 108
Frequency
8
9
7
12
11
6
5
13
(v)
Class-Interval
28 - 38
38 - 48
48 - 58
58 - 68
68 - 78
78 - 88
88 - 98
98 - 108
Frequency
8
9
5
12
13
6
5
13
Question
15
15.
During the medical check-up of 79 students of a class, their weights in kgs are recorded as follows.
Identify the number of students whose weight is more than 49 kg
Class-Interval
39 - 44
44 - 49
49 - 54
54 - 59
59 - 64
64 - 69
69 - 74
74 - 79
Frequency
10
10
7
11
10
12
8
11
(i)
58
(ii)
61
(iii)
59
(iv)
56
(v)
60
Assignment Key
1) (ii)
2) (ii)
3) (v)
4) (iv)
5) (iv)
6) (iii)
7) (i)
8) (iii)
9) (ii)
10) (iv)
11) (iii)
12) (i)
13) (v)
14) (iii)
15) (iii)
