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 - 19
11
20 - 28
17
29 - 37
29
38 - 46
40
47 - 55
52
56 - 64
64
(i)
Class-Interval
11 - 19
20 - 28
29 - 37
38 - 46
47 - 55
56 - 64
Frequency
11
12
6
11
12
12
(ii)
Class-Interval
11 - 19
20 - 28
29 - 37
38 - 46
47 - 55
56 - 64
Frequency
11
6
12
13
12
12
(iii)
Class-Interval
11 - 19
20 - 28
29 - 37
38 - 46
47 - 55
56 - 64
Frequency
11
6
12
11
12
12
(iv)
Class-Interval
11 - 19
20 - 28
29 - 37
38 - 46
47 - 55
56 - 64
Frequency
11
6
10
11
12
12
(v)
Class-Interval
11 - 19
20 - 28
29 - 37
38 - 46
47 - 55
56 - 64
Frequency
11
12
12
11
12
6
Question
2
2.
Construct a frequency distribution table from the following cumulative frequency distribution
Class-Interval
Cumulative Frequency
15 - 25
15
25 - 35
21
35 - 45
33
45 - 55
41
55 - 65
47
(i)
Class-Interval
15 - 25
25 - 35
35 - 45
45 - 55
55 - 65
Frequency
15
12
6
8
6
(ii)
Class-Interval
15 - 25
25 - 35
35 - 45
45 - 55
55 - 65
Frequency
15
6
10
8
6
(iii)
Class-Interval
15 - 25
25 - 35
35 - 45
45 - 55
55 - 65
Frequency
15
4
12
8
6
(iv)
Class-Interval
15 - 25
25 - 35
35 - 45
45 - 55
55 - 65
Frequency
15
6
12
8
6
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)
10 - 15
16 - 21
22 - 27
28 - 33
34 - 39
40 - 45
46 - 51
52 - 57
No. of Patients
13
26
49
87
19
69
70
16
(i)
Age (in years)
Cumulative Frequency
10 - 15
13
16 - 21
29
22 - 27
78
28 - 33
165
34 - 39
184
40 - 45
253
46 - 51
323
52 - 57
349
(ii)
Age (in years)
Cumulative Frequency
10 - 15
13
16 - 21
39
22 - 27
126
28 - 33
175
34 - 39
194
40 - 45
263
46 - 51
333
52 - 57
349
(iii)
Age (in years)
Cumulative Frequency
10 - 15
13
16 - 21
39
22 - 27
88
28 - 33
175
34 - 39
191
40 - 45
260
46 - 51
330
52 - 57
346
(iv)
Age (in years)
Cumulative Frequency
10 - 15
13
16 - 21
39
22 - 27
83
28 - 33
170
34 - 39
189
40 - 45
258
46 - 51
328
52 - 57
344
(v)
Age (in years)
Cumulative Frequency
10 - 15
13
16 - 21
39
22 - 27
88
28 - 33
175
34 - 39
194
40 - 45
263
46 - 51
333
52 - 57
349
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
No. of Patients
33
41
21
81
(i)
Age (in years)
Cumulative Frequency
20 - 30
81
30 - 40
122
40 - 50
143
50 - 60
176
(ii)
Age (in years)
Cumulative Frequency
20 - 30
33
30 - 40
74
40 - 50
90
50 - 60
171
(iii)
Age (in years)
Cumulative Frequency
20 - 30
33
30 - 40
74
40 - 50
95
50 - 60
176
(iv)
Age (in years)
Cumulative Frequency
20 - 30
33
30 - 40
76
40 - 50
97
50 - 60
178
(v)
Age (in years)
Cumulative Frequency
20 - 30
33
30 - 40
54
40 - 50
95
50 - 60
176
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)
200 - 230
231 - 261
262 - 292
293 - 323
324 - 354
355 - 385
Labourers
12
4
17
16
13
20
(i)
Wages (in rupees)
Cumulative Frequency
200 - 230
12
231 - 261
16
262 - 292
29
293 - 323
45
324 - 354
58
355 - 385
78
(ii)
Wages (in rupees)
Cumulative Frequency
200 - 230
12
231 - 261
29
262 - 292
33
293 - 323
49
324 - 354
62
355 - 385
82
(iii)
Wages (in rupees)
Cumulative Frequency
200 - 230
12
231 - 261
16
262 - 292
33
293 - 323
45
324 - 354
58
355 - 385
78
(iv)
Wages (in rupees)
Cumulative Frequency
200 - 230
12
231 - 261
32
262 - 292
49
293 - 323
65
324 - 354
78
355 - 385
82
(v)
Wages (in rupees)
Cumulative Frequency
200 - 230
12
231 - 261
16
262 - 292
33
293 - 323
49
324 - 354
62
355 - 385
82
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
12
13
9
1
11
9
(i)
Wages (in rupees)
Cumulative Frequency
200 - 220
12
220 - 240
21
240 - 260
30
260 - 280
31
280 - 300
42
300 - 320
55
(ii)
Wages (in rupees)
Cumulative Frequency
200 - 220
12
220 - 240
25
240 - 260
34
260 - 280
35
280 - 300
46
300 - 320
55
(iii)
Wages (in rupees)
Cumulative Frequency
200 - 220
12
220 - 240
21
240 - 260
34
260 - 280
35
280 - 300
46
300 - 320
55
(iv)
Wages (in rupees)
Cumulative Frequency
200 - 220
12
220 - 240
25
240 - 260
29
260 - 280
30
280 - 300
41
300 - 320
50
(v)
Wages (in rupees)
Cumulative Frequency
200 - 220
12
220 - 240
25
240 - 260
34
260 - 280
38
280 - 300
49
300 - 320
58
Question
7
7.
Identify the cumulative frequency of the given grouped data.
class interval
22 - 31
32 - 41
42 - 51
52 - 61
62 - 71
72 - 81
82 - 91
frequency
11
11
17
23
25
21
13
(i)
class interval
Cumulative Frequency
22 - 31
11
32 - 41
24
42 - 51
41
52 - 61
64
62 - 71
89
72 - 81
110
82 - 91
121
(ii)
class interval
Cumulative Frequency
22 - 31
11
32 - 41
28
42 - 51
39
52 - 61
62
62 - 71
87
72 - 81
108
82 - 91
121
(iii)
class interval
Cumulative Frequency
22 - 31
11
32 - 41
22
42 - 51
34
52 - 61
57
62 - 71
82
72 - 81
103
82 - 91
116
(iv)
class interval
Cumulative Frequency
22 - 31
11
32 - 41
22
42 - 51
39
52 - 61
62
62 - 71
87
72 - 81
108
82 - 91
121
(v)
class interval
Cumulative Frequency
22 - 31
11
32 - 41
22
42 - 51
39
52 - 61
64
62 - 71
89
72 - 81
110
82 - 91
123
Question
8
8.
Identify the cumulative frequency of the given grouped data.
class interval
46 - 53
53 - 60
60 - 67
67 - 74
74 - 81
frequency
13
14
11
14
23
(i)
class interval
Cumulative Frequency
46 - 53
13
53 - 60
36
60 - 67
47
67 - 74
61
74 - 81
75
(ii)
class interval
Cumulative Frequency
46 - 53
13
53 - 60
27
60 - 67
38
67 - 74
52
74 - 81
75
(iii)
class interval
Cumulative Frequency
46 - 53
13
53 - 60
31
60 - 67
42
67 - 74
56
74 - 81
79
(iv)
class interval
Cumulative Frequency
46 - 53
13
53 - 60
24
60 - 67
38
67 - 74
52
74 - 81
75
(v)
class interval
Cumulative Frequency
46 - 53
13
53 - 60
27
60 - 67
36
67 - 74
50
74 - 81
73
Question
9
9.
Less than cumulative curves are drawn using
(i)
lower boundaries of classes and greater than cumulative frequencies
(ii)
mid values of classes and less 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)
lower boundaries of classes and greater than cumulative frequencies
(ii)
upper 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
76
-
85
.
Class-Interval
46 - 55
56 - 65
66 - 75
76 - 85
86 - 95
Frequency
20
6
7
11
22
(i)
45
(ii)
42
(iii)
44
(iv)
46
(v)
43
Question
12
12.
Find the cumulative frequency of class
68
-
75
.
Class-Interval
40 - 47
47 - 54
54 - 61
61 - 68
68 - 75
75 - 82
Frequency
22
23
15
18
16
25
(i)
95
(ii)
94
(iii)
92
(iv)
93
(v)
96
Question
13
13.
The following cumulative frequency table represents which of the following frequency distribution
Class-Interval
Cumulative Frequency
29 - 35
10
35 - 41
26
41 - 47
41
47 - 53
54
53 - 59
62
(i)
Class-Interval
29 - 35
35 - 41
41 - 47
47 - 53
53 - 59
Frequency
10
15
16
13
8
(ii)
Class-Interval
29 - 35
35 - 41
41 - 47
47 - 53
53 - 59
Frequency
10
18
15
13
8
(iii)
Class-Interval
29 - 35
35 - 41
41 - 47
47 - 53
53 - 59
Frequency
10
16
20
13
8
(iv)
Class-Interval
29 - 35
35 - 41
41 - 47
47 - 53
53 - 59
Frequency
10
8
15
13
16
(v)
Class-Interval
29 - 35
35 - 41
41 - 47
47 - 53
53 - 59
Frequency
10
16
15
13
8
Question
14
14.
The following cumulative frequency table represents which of the following frequency distribution
Class-Interval
Cumulative Frequency
37 - 45
53
45 - 53
42
53 - 61
31
61 - 69
26
69 - 77
13
(i)
Class-Interval
37 - 45
45 - 53
53 - 61
61 - 69
69 - 77
Frequency
11
11
7
13
13
(ii)
Class-Interval
37 - 45
45 - 53
53 - 61
61 - 69
69 - 77
Frequency
11
14
5
13
13
(iii)
Class-Interval
37 - 45
45 - 53
53 - 61
61 - 69
69 - 77
Frequency
11
5
11
13
13
(iv)
Class-Interval
37 - 45
45 - 53
53 - 61
61 - 69
69 - 77
Frequency
11
13
5
13
11
(v)
Class-Interval
37 - 45
45 - 53
53 - 61
61 - 69
69 - 77
Frequency
11
11
5
13
13
Question
15
15.
During the medical check-up of 73 students of a class, their weights in kgs are recorded as follows.
Identify the number of students whose weight is more than 80 kg
Class-Interval
35 - 44
44 - 53
53 - 62
62 - 71
71 - 80
80 - 89
89 - 98
98 - 107
Frequency
12
11
7
6
11
9
8
9
(i)
24
(ii)
29
(iii)
27
(iv)
26
(v)
25
Assignment Key
1) (iii)
2) (iv)
3) (v)
4) (iii)
5) (v)
6) (ii)
7) (iv)
8) (ii)
9) (iv)
10) (i)
11) (iii)
12) (ii)
13) (v)
14) (v)
15) (iv)
