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
33 - 40
5
41 - 48
12
49 - 56
23
57 - 64
33
65 - 72
44
73 - 80
54
81 - 88
69
(i)
Class-Interval
33 - 40
41 - 48
49 - 56
57 - 64
65 - 72
73 - 80
81 - 88
Frequency
5
15
11
10
11
10
7
(ii)
Class-Interval
33 - 40
41 - 48
49 - 56
57 - 64
65 - 72
73 - 80
81 - 88
Frequency
5
7
14
10
11
10
15
(iii)
Class-Interval
33 - 40
41 - 48
49 - 56
57 - 64
65 - 72
73 - 80
81 - 88
Frequency
5
7
11
12
11
10
15
(iv)
Class-Interval
33 - 40
41 - 48
49 - 56
57 - 64
65 - 72
73 - 80
81 - 88
Frequency
5
7
11
10
11
10
15
(v)
Class-Interval
33 - 40
41 - 48
49 - 56
57 - 64
65 - 72
73 - 80
81 - 88
Frequency
5
11
7
10
11
10
15
Question
2
2.
Construct a frequency distribution table from the following cumulative frequency distribution
Class-Interval
Cumulative Frequency
18 - 25
14
25 - 32
27
32 - 39
36
39 - 46
42
46 - 53
58
53 - 60
69
60 - 67
74
(i)
Class-Interval
18 - 25
25 - 32
32 - 39
39 - 46
46 - 53
53 - 60
60 - 67
Frequency
14
13
9
6
16
11
5
(ii)
Class-Interval
18 - 25
25 - 32
32 - 39
39 - 46
46 - 53
53 - 60
60 - 67
Frequency
14
5
9
6
16
11
13
(iii)
Class-Interval
18 - 25
25 - 32
32 - 39
39 - 46
46 - 53
53 - 60
60 - 67
Frequency
14
13
9
10
16
11
5
(iv)
Class-Interval
18 - 25
25 - 32
32 - 39
39 - 46
46 - 53
53 - 60
60 - 67
Frequency
14
9
13
6
16
11
5
(v)
Class-Interval
18 - 25
25 - 32
32 - 39
39 - 46
46 - 53
53 - 60
60 - 67
Frequency
14
13
14
6
16
11
5
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
86 - 96
No. of Patients
90
72
70
32
51
48
28
(i)
Age (in years)
Cumulative Frequency
20 - 30
90
31 - 41
162
42 - 52
232
53 - 63
261
64 - 74
312
75 - 85
360
86 - 96
388
(ii)
Age (in years)
Cumulative Frequency
20 - 30
90
31 - 41
162
42 - 52
230
53 - 63
262
64 - 74
313
75 - 85
361
86 - 96
389
(iii)
Age (in years)
Cumulative Frequency
20 - 30
90
31 - 41
118
42 - 52
188
53 - 63
220
64 - 74
271
75 - 85
319
86 - 96
391
(iv)
Age (in years)
Cumulative Frequency
20 - 30
90
31 - 41
160
42 - 52
232
53 - 63
264
64 - 74
315
75 - 85
363
86 - 96
391
(v)
Age (in years)
Cumulative Frequency
20 - 30
90
31 - 41
162
42 - 52
232
53 - 63
264
64 - 74
315
75 - 85
363
86 - 96
391
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 - 25
25 - 30
30 - 35
35 - 40
40 - 45
45 - 50
50 - 55
55 - 60
No. of Patients
88
11
78
32
49
55
39
19
(i)
Age (in years)
Cumulative Frequency
20 - 25
88
25 - 30
107
30 - 35
185
35 - 40
217
40 - 45
266
45 - 50
321
50 - 55
360
55 - 60
371
(ii)
Age (in years)
Cumulative Frequency
20 - 25
88
25 - 30
99
30 - 35
177
35 - 40
209
40 - 45
260
45 - 50
315
50 - 55
354
55 - 60
373
(iii)
Age (in years)
Cumulative Frequency
20 - 25
88
25 - 30
99
30 - 35
177
35 - 40
209
40 - 45
258
45 - 50
313
50 - 55
352
55 - 60
371
(iv)
Age (in years)
Cumulative Frequency
20 - 25
88
25 - 30
99
30 - 35
131
35 - 40
209
40 - 45
258
45 - 50
313
50 - 55
352
55 - 60
371
(v)
Age (in years)
Cumulative Frequency
20 - 25
88
25 - 30
99
30 - 35
182
35 - 40
214
40 - 45
263
45 - 50
318
50 - 55
357
55 - 60
376
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
14
18
19
13
9
4
(i)
Wages (in rupees)
Cumulative Frequency
300 - 320
14
321 - 341
33
342 - 362
51
363 - 383
64
384 - 404
73
405 - 425
77
(ii)
Wages (in rupees)
Cumulative Frequency
300 - 320
14
321 - 341
32
342 - 362
47
363 - 383
60
384 - 404
69
405 - 425
73
(iii)
Wages (in rupees)
Cumulative Frequency
300 - 320
14
321 - 341
18
342 - 362
37
363 - 383
50
384 - 404
59
405 - 425
77
(iv)
Wages (in rupees)
Cumulative Frequency
300 - 320
14
321 - 341
32
342 - 362
51
363 - 383
64
384 - 404
73
405 - 425
77
(v)
Wages (in rupees)
Cumulative Frequency
300 - 320
14
321 - 341
32
342 - 362
51
363 - 383
66
384 - 404
75
405 - 425
79
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
4
12
10
5
7
15
(i)
Wages (in rupees)
Cumulative Frequency
200 - 220
4
220 - 240
16
240 - 260
28
260 - 280
33
280 - 300
40
300 - 320
55
(ii)
Wages (in rupees)
Cumulative Frequency
200 - 220
4
220 - 240
16
240 - 260
26
260 - 280
31
280 - 300
38
300 - 320
53
(iii)
Wages (in rupees)
Cumulative Frequency
200 - 220
4
220 - 240
19
240 - 260
29
260 - 280
34
280 - 300
41
300 - 320
53
(iv)
Wages (in rupees)
Cumulative Frequency
200 - 220
4
220 - 240
14
240 - 260
26
260 - 280
31
280 - 300
38
300 - 320
53
(v)
Wages (in rupees)
Cumulative Frequency
200 - 220
4
220 - 240
16
240 - 260
26
260 - 280
29
280 - 300
36
300 - 320
51
Question
7
7.
Identify the cumulative frequency of the given grouped data.
class interval
17 - 23
24 - 30
31 - 37
38 - 44
45 - 51
52 - 58
frequency
12
11
23
18
10
7
(i)
class interval
Cumulative Frequency
17 - 23
12
24 - 30
23
31 - 37
46
38 - 44
64
45 - 51
74
52 - 58
81
(ii)
class interval
Cumulative Frequency
17 - 23
12
24 - 30
19
31 - 37
42
38 - 44
60
45 - 51
70
52 - 58
81
(iii)
class interval
Cumulative Frequency
17 - 23
12
24 - 30
23
31 - 37
46
38 - 44
60
45 - 51
70
52 - 58
77
(iv)
class interval
Cumulative Frequency
17 - 23
12
24 - 30
23
31 - 37
42
38 - 44
60
45 - 51
70
52 - 58
77
(v)
class interval
Cumulative Frequency
17 - 23
12
24 - 30
35
31 - 37
46
38 - 44
64
45 - 51
74
52 - 58
81
Question
8
8.
Identify the cumulative frequency of the given grouped data.
class interval
21 - 28
28 - 35
35 - 42
42 - 49
49 - 56
56 - 63
63 - 70
70 - 77
frequency
7
22
12
19
9
21
8
16
(i)
class interval
Cumulative Frequency
21 - 28
7
28 - 35
29
35 - 42
41
42 - 49
60
49 - 56
66
56 - 63
87
63 - 70
95
70 - 77
111
(ii)
class interval
Cumulative Frequency
21 - 28
7
28 - 35
29
35 - 42
41
42 - 49
60
49 - 56
69
56 - 63
90
63 - 70
98
70 - 77
114
(iii)
class interval
Cumulative Frequency
21 - 28
7
28 - 35
29
35 - 42
38
42 - 49
57
49 - 56
66
56 - 63
87
63 - 70
95
70 - 77
111
(iv)
class interval
Cumulative Frequency
21 - 28
7
28 - 35
23
35 - 42
35
42 - 49
54
49 - 56
63
56 - 63
84
63 - 70
92
70 - 77
114
(v)
class interval
Cumulative Frequency
21 - 28
7
28 - 35
29
35 - 42
48
42 - 49
60
49 - 56
69
56 - 63
90
63 - 70
98
70 - 77
114
Question
9
9.
Less than cumulative curves are drawn using
(i)
upper boundaries of classes and less than cumulative frequencies
(ii)
lower boundaries of classes and less than cumulative frequencies
(iii)
mid values of classes and less than cumulative frequencies
(iv)
lower boundaries of classes and greater than cumulative frequencies
Question
10
10.
Greater than cumulative curves are drawn using
(i)
upper boundaries of classes and less than cumulative frequencies
(ii)
mid values of classes and greater than cumulative frequencies
(iii)
upper boundaries 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
64
-
72
.
Class-Interval
28 - 36
37 - 45
46 - 54
55 - 63
64 - 72
73 - 81
Frequency
20
21
24
15
12
6
(i)
93
(ii)
90
(iii)
95
(iv)
91
(v)
92
Question
12
12.
Find the cumulative frequency of class
25
-
31
.
Class-Interval
19 - 25
25 - 31
31 - 37
37 - 43
Frequency
13
19
16
6
(i)
29
(ii)
31
(iii)
33
(iv)
34
(v)
32
Question
13
13.
The following cumulative frequency table represents which of the following frequency distribution
Class-Interval
Cumulative Frequency
25 - 35
16
35 - 45
30
45 - 55
40
55 - 65
47
65 - 75
56
75 - 85
71
85 - 95
79
95 - 105
92
(i)
Class-Interval
25 - 35
35 - 45
45 - 55
55 - 65
65 - 75
75 - 85
85 - 95
95 - 105
Frequency
16
14
10
7
12
15
8
13
(ii)
Class-Interval
25 - 35
35 - 45
45 - 55
55 - 65
65 - 75
75 - 85
85 - 95
95 - 105
Frequency
16
14
7
10
9
15
8
13
(iii)
Class-Interval
25 - 35
35 - 45
45 - 55
55 - 65
65 - 75
75 - 85
85 - 95
95 - 105
Frequency
16
14
10
7
9
15
8
13
(iv)
Class-Interval
25 - 35
35 - 45
45 - 55
55 - 65
65 - 75
75 - 85
85 - 95
95 - 105
Frequency
16
14
8
7
9
15
8
13
(v)
Class-Interval
25 - 35
35 - 45
45 - 55
55 - 65
65 - 75
75 - 85
85 - 95
95 - 105
Frequency
16
13
10
7
9
15
8
14
Question
14
14.
The following cumulative frequency table represents which of the following frequency distribution
Class-Interval
Cumulative Frequency
11 - 21
102
21 - 31
89
31 - 41
74
41 - 51
58
51 - 61
52
61 - 71
38
71 - 81
25
81 - 91
16
(i)
Class-Interval
11 - 21
21 - 31
31 - 41
41 - 51
51 - 61
61 - 71
71 - 81
81 - 91
Frequency
13
15
14
6
14
13
9
16
(ii)
Class-Interval
11 - 21
21 - 31
31 - 41
41 - 51
51 - 61
61 - 71
71 - 81
81 - 91
Frequency
13
15
6
16
14
13
9
16
(iii)
Class-Interval
11 - 21
21 - 31
31 - 41
41 - 51
51 - 61
61 - 71
71 - 81
81 - 91
Frequency
13
15
16
6
10
13
9
16
(iv)
Class-Interval
11 - 21
21 - 31
31 - 41
41 - 51
51 - 61
61 - 71
71 - 81
81 - 91
Frequency
13
15
16
6
14
13
9
16
(v)
Class-Interval
11 - 21
21 - 31
31 - 41
41 - 51
51 - 61
61 - 71
71 - 81
81 - 91
Frequency
13
16
16
6
14
13
9
15
Question
15
15.
During the medical check-up of 62 students of a class, their weights in kgs are recorded as follows.
Identify the number of students whose weight is more than 43 kg
Class-Interval
37 - 43
43 - 49
49 - 55
55 - 61
61 - 67
67 - 73
73 - 79
79 - 85
Frequency
6
7
5
5
6
12
10
11
(i)
57
(ii)
56
(iii)
59
(iv)
53
(v)
55
Assignment Key
1) (iv)
2) (i)
3) (v)
4) (iii)
5) (iv)
6) (ii)
7) (i)
8) (ii)
9) (i)
10) (iv)
11) (v)
12) (v)
13) (iii)
14) (iv)
15) (ii)
