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
19 - 28
8
29 - 38
15
39 - 48
20
49 - 58
32
59 - 68
46
69 - 78
55
79 - 88
66
89 - 98
77
(i)
Class-Interval
19 - 28
29 - 38
39 - 48
49 - 58
59 - 68
69 - 78
79 - 88
89 - 98
Frequency
8
7
12
5
14
9
11
11
(ii)
Class-Interval
19 - 28
29 - 38
39 - 48
49 - 58
59 - 68
69 - 78
79 - 88
89 - 98
Frequency
8
7
5
12
14
9
11
11
(iii)
Class-Interval
19 - 28
29 - 38
39 - 48
49 - 58
59 - 68
69 - 78
79 - 88
89 - 98
Frequency
8
11
5
12
14
9
11
7
(iv)
Class-Interval
19 - 28
29 - 38
39 - 48
49 - 58
59 - 68
69 - 78
79 - 88
89 - 98
Frequency
8
7
1
12
14
9
11
11
(v)
Class-Interval
19 - 28
29 - 38
39 - 48
49 - 58
59 - 68
69 - 78
79 - 88
89 - 98
Frequency
8
7
5
12
9
9
11
11
Question
2
2.
Construct a frequency distribution table from the following cumulative frequency distribution
Class-Interval
Cumulative Frequency
28 - 35
9
35 - 42
17
42 - 49
29
49 - 56
40
56 - 63
56
63 - 70
69
(i)
Class-Interval
28 - 35
35 - 42
42 - 49
49 - 56
56 - 63
63 - 70
Frequency
9
8
12
11
16
13
(ii)
Class-Interval
28 - 35
35 - 42
42 - 49
49 - 56
56 - 63
63 - 70
Frequency
9
12
8
11
16
13
(iii)
Class-Interval
28 - 35
35 - 42
42 - 49
49 - 56
56 - 63
63 - 70
Frequency
9
8
12
13
16
13
(iv)
Class-Interval
28 - 35
35 - 42
42 - 49
49 - 56
56 - 63
63 - 70
Frequency
9
8
14
11
16
13
(v)
Class-Interval
28 - 35
35 - 42
42 - 49
49 - 56
56 - 63
63 - 70
Frequency
9
13
12
11
16
8
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
12
81
40
23
38
13
50
60
(i)
Age (in years)
Cumulative Frequency
20 - 25
12
26 - 31
93
32 - 37
116
38 - 43
156
44 - 49
194
50 - 55
207
56 - 61
257
62 - 67
317
(ii)
Age (in years)
Cumulative Frequency
20 - 25
12
26 - 31
93
32 - 37
133
38 - 43
156
44 - 49
194
50 - 55
207
56 - 61
257
62 - 67
317
(iii)
Age (in years)
Cumulative Frequency
20 - 25
12
26 - 31
93
32 - 37
133
38 - 43
156
44 - 49
199
50 - 55
212
56 - 61
262
62 - 67
322
(iv)
Age (in years)
Cumulative Frequency
20 - 25
12
26 - 31
93
32 - 37
130
38 - 43
153
44 - 49
191
50 - 55
204
56 - 61
254
62 - 67
314
(v)
Age (in years)
Cumulative Frequency
20 - 25
12
26 - 31
72
32 - 37
112
38 - 43
135
44 - 49
173
50 - 55
186
56 - 61
236
62 - 67
317
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
30 - 35
35 - 40
40 - 45
45 - 50
No. of Patients
52
11
46
85
27
41
64
80
(i)
Age (in years)
Cumulative Frequency
10 - 15
52
15 - 20
63
20 - 25
109
25 - 30
194
30 - 35
221
35 - 40
262
40 - 45
326
45 - 50
406
(ii)
Age (in years)
Cumulative Frequency
10 - 15
52
15 - 20
63
20 - 25
148
25 - 30
194
30 - 35
221
35 - 40
262
40 - 45
326
45 - 50
406
(iii)
Age (in years)
Cumulative Frequency
10 - 15
52
15 - 20
63
20 - 25
107
25 - 30
192
30 - 35
219
35 - 40
260
40 - 45
324
45 - 50
404
(iv)
Age (in years)
Cumulative Frequency
10 - 15
52
15 - 20
63
20 - 25
109
25 - 30
194
30 - 35
223
35 - 40
264
40 - 45
328
45 - 50
408
(v)
Age (in years)
Cumulative Frequency
10 - 15
52
15 - 20
132
20 - 25
178
25 - 30
263
30 - 35
290
35 - 40
331
40 - 45
395
45 - 50
406
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
17
9
13
6
6
2
(i)
Wages (in rupees)
Cumulative Frequency
300 - 320
17
321 - 341
19
342 - 362
32
363 - 383
38
384 - 404
44
405 - 425
53
(ii)
Wages (in rupees)
Cumulative Frequency
300 - 320
17
321 - 341
26
342 - 362
44
363 - 383
50
384 - 404
56
405 - 425
58
(iii)
Wages (in rupees)
Cumulative Frequency
300 - 320
17
321 - 341
26
342 - 362
39
363 - 383
42
384 - 404
48
405 - 425
50
(iv)
Wages (in rupees)
Cumulative Frequency
300 - 320
17
321 - 341
26
342 - 362
39
363 - 383
45
384 - 404
51
405 - 425
53
(v)
Wages (in rupees)
Cumulative Frequency
300 - 320
17
321 - 341
30
342 - 362
39
363 - 383
45
384 - 404
51
405 - 425
53
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
16
20
8
18
14
13
(i)
Wages (in rupees)
Cumulative Frequency
300 - 330
16
330 - 360
36
360 - 390
44
390 - 420
59
420 - 450
73
450 - 480
86
(ii)
Wages (in rupees)
Cumulative Frequency
300 - 330
16
330 - 360
36
360 - 390
44
390 - 420
62
420 - 450
76
450 - 480
89
(iii)
Wages (in rupees)
Cumulative Frequency
300 - 330
16
330 - 360
36
360 - 390
48
390 - 420
66
420 - 450
80
450 - 480
93
(iv)
Wages (in rupees)
Cumulative Frequency
300 - 330
16
330 - 360
29
360 - 390
37
390 - 420
55
420 - 450
69
450 - 480
89
(v)
Wages (in rupees)
Cumulative Frequency
300 - 330
16
330 - 360
24
360 - 390
44
390 - 420
62
420 - 450
76
450 - 480
89
Question
7
7.
Identify the cumulative frequency of the given grouped data.
class interval
35 - 40
41 - 46
47 - 52
53 - 58
59 - 64
65 - 70
71 - 76
77 - 82
frequency
13
16
18
12
8
19
25
23
(i)
class interval
Cumulative Frequency
35 - 40
13
41 - 46
36
47 - 52
54
53 - 58
66
59 - 64
74
65 - 70
93
71 - 76
118
77 - 82
134
(ii)
class interval
Cumulative Frequency
35 - 40
13
41 - 46
29
47 - 52
47
53 - 58
59
59 - 64
65
65 - 70
84
71 - 76
109
77 - 82
132
(iii)
class interval
Cumulative Frequency
35 - 40
13
41 - 46
29
47 - 52
47
53 - 58
59
59 - 64
67
65 - 70
86
71 - 76
111
77 - 82
134
(iv)
class interval
Cumulative Frequency
35 - 40
13
41 - 46
29
47 - 52
41
53 - 58
59
59 - 64
67
65 - 70
86
71 - 76
111
77 - 82
134
(v)
class interval
Cumulative Frequency
35 - 40
13
41 - 46
29
47 - 52
45
53 - 58
57
59 - 64
65
65 - 70
84
71 - 76
109
77 - 82
132
Question
8
8.
Identify the cumulative frequency of the given grouped data.
class interval
15 - 20
20 - 25
25 - 30
30 - 35
frequency
23
21
6
11
(i)
class interval
Cumulative Frequency
15 - 20
23
20 - 25
44
25 - 30
50
30 - 35
61
(ii)
class interval
Cumulative Frequency
15 - 20
23
20 - 25
29
25 - 30
50
30 - 35
61
(iii)
class interval
Cumulative Frequency
15 - 20
11
20 - 25
32
25 - 30
38
30 - 35
61
(iv)
class interval
Cumulative Frequency
15 - 20
23
20 - 25
47
25 - 30
53
30 - 35
64
(v)
class interval
Cumulative Frequency
15 - 20
23
20 - 25
44
25 - 30
52
30 - 35
63
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)
lower boundaries 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)
mid values of classes and greater than cumulative frequencies
(ii)
lower boundaries of classes and greater than cumulative frequencies
(iii)
upper boundaries of classes and greater than cumulative frequencies
(iv)
upper boundaries of classes and less than cumulative frequencies
Question
11
11.
Find the cumulative frequency of class
51
-
57
.
Class-Interval
23 - 29
30 - 36
37 - 43
44 - 50
51 - 57
Frequency
13
14
21
24
20
(i)
89
(ii)
95
(iii)
91
(iv)
93
(v)
92
Question
12
12.
Find the cumulative frequency of class
57
-
65
.
Class-Interval
41 - 49
49 - 57
57 - 65
65 - 73
73 - 81
81 - 89
89 - 97
Frequency
17
22
12
9
6
5
5
(i)
53
(ii)
50
(iii)
49
(iv)
51
(v)
52
Question
13
13.
The following cumulative frequency table represents which of the following frequency distribution
Class-Interval
Cumulative Frequency
33 - 43
7
43 - 53
16
53 - 63
32
63 - 73
38
73 - 83
46
83 - 93
61
(i)
Class-Interval
33 - 43
43 - 53
53 - 63
63 - 73
73 - 83
83 - 93
Frequency
7
9
16
6
8
15
(ii)
Class-Interval
33 - 43
43 - 53
53 - 63
63 - 73
73 - 83
83 - 93
Frequency
7
16
9
6
8
15
(iii)
Class-Interval
33 - 43
43 - 53
53 - 63
63 - 73
73 - 83
83 - 93
Frequency
7
9
13
6
8
15
(iv)
Class-Interval
33 - 43
43 - 53
53 - 63
63 - 73
73 - 83
83 - 93
Frequency
7
9
16
10
8
15
(v)
Class-Interval
33 - 43
43 - 53
53 - 63
63 - 73
73 - 83
83 - 93
Frequency
7
15
16
6
8
9
Question
14
14.
The following cumulative frequency table represents which of the following frequency distribution
Class-Interval
Cumulative Frequency
21 - 25
90
25 - 29
81
29 - 33
73
33 - 37
59
37 - 41
51
41 - 45
35
45 - 49
20
49 - 53
11
(i)
Class-Interval
21 - 25
25 - 29
29 - 33
33 - 37
37 - 41
41 - 45
45 - 49
49 - 53
Frequency
9
11
14
8
16
15
9
8
(ii)
Class-Interval
21 - 25
25 - 29
29 - 33
33 - 37
37 - 41
41 - 45
45 - 49
49 - 53
Frequency
9
8
14
8
20
15
9
11
(iii)
Class-Interval
21 - 25
25 - 29
29 - 33
33 - 37
37 - 41
41 - 45
45 - 49
49 - 53
Frequency
9
8
16
8
16
15
9
11
(iv)
Class-Interval
21 - 25
25 - 29
29 - 33
33 - 37
37 - 41
41 - 45
45 - 49
49 - 53
Frequency
9
8
8
14
16
15
9
11
(v)
Class-Interval
21 - 25
25 - 29
29 - 33
33 - 37
37 - 41
41 - 45
45 - 49
49 - 53
Frequency
9
8
14
8
16
15
9
11
Question
15
15.
During the medical check-up of 57 students of a class, their weights in kgs are recorded as follows.
Identify the number of students whose weight is more than 88 kg
Class-Interval
40 - 48
48 - 56
56 - 64
64 - 72
72 - 80
80 - 88
88 - 96
Frequency
5
10
7
7
8
8
12
(i)
10
(ii)
13
(iii)
12
(iv)
11
(v)
14
Assignment Key
1) (ii)
2) (i)
3) (ii)
4) (i)
5) (iv)
6) (ii)
7) (iii)
8) (i)
9) (iv)
10) (ii)
11) (v)
12) (iv)
13) (i)
14) (v)
15) (iii)
