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
29 - 33
5
34 - 38
12
39 - 43
19
44 - 48
33
49 - 53
44
54 - 58
53
(i)
Class-Interval
29 - 33
34 - 38
39 - 43
44 - 48
49 - 53
54 - 58
Frequency
5
7
5
14
11
9
(ii)
Class-Interval
29 - 33
34 - 38
39 - 43
44 - 48
49 - 53
54 - 58
Frequency
5
7
7
12
11
9
(iii)
Class-Interval
29 - 33
34 - 38
39 - 43
44 - 48
49 - 53
54 - 58
Frequency
5
7
7
14
11
9
(iv)
Class-Interval
29 - 33
34 - 38
39 - 43
44 - 48
49 - 53
54 - 58
Frequency
5
9
7
14
11
7
Question
2
2.
Construct a frequency distribution table from the following cumulative frequency distribution
Class-Interval
Cumulative Frequency
12 - 16
10
16 - 20
16
20 - 24
26
24 - 28
32
28 - 32
46
(i)
Class-Interval
12 - 16
16 - 20
20 - 24
24 - 28
28 - 32
Frequency
10
10
6
6
14
(ii)
Class-Interval
12 - 16
16 - 20
20 - 24
24 - 28
28 - 32
Frequency
10
6
13
6
14
(iii)
Class-Interval
12 - 16
16 - 20
20 - 24
24 - 28
28 - 32
Frequency
10
6
10
6
14
(iv)
Class-Interval
12 - 16
16 - 20
20 - 24
24 - 28
28 - 32
Frequency
10
14
10
6
6
(v)
Class-Interval
12 - 16
16 - 20
20 - 24
24 - 28
28 - 32
Frequency
10
11
10
6
14
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 - 20
21 - 31
32 - 42
43 - 53
54 - 64
65 - 75
76 - 86
87 - 97
No. of Patients
37
51
35
53
55
18
90
19
(i)
Age (in years)
Cumulative Frequency
10 - 20
37
21 - 31
88
32 - 42
121
43 - 53
174
54 - 64
229
65 - 75
247
76 - 86
337
87 - 97
356
(ii)
Age (in years)
Cumulative Frequency
10 - 20
37
21 - 31
56
32 - 42
91
43 - 53
144
54 - 64
199
65 - 75
217
76 - 86
307
87 - 97
358
(iii)
Age (in years)
Cumulative Frequency
10 - 20
37
21 - 31
88
32 - 42
123
43 - 53
176
54 - 64
231
65 - 75
249
76 - 86
339
87 - 97
358
(iv)
Age (in years)
Cumulative Frequency
10 - 20
37
21 - 31
88
32 - 42
123
43 - 53
176
54 - 64
234
65 - 75
252
76 - 86
342
87 - 97
361
(v)
Age (in years)
Cumulative Frequency
10 - 20
37
21 - 31
88
32 - 42
141
43 - 53
176
54 - 64
231
65 - 75
249
76 - 86
339
87 - 97
358
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
52
37
54
36
(i)
Age (in years)
Cumulative Frequency
20 - 30
52
30 - 40
106
40 - 50
143
50 - 60
179
(ii)
Age (in years)
Cumulative Frequency
20 - 30
52
30 - 40
92
40 - 50
146
50 - 60
182
(iii)
Age (in years)
Cumulative Frequency
20 - 30
52
30 - 40
89
40 - 50
140
50 - 60
176
(iv)
Age (in years)
Cumulative Frequency
20 - 30
36
30 - 40
73
40 - 50
127
50 - 60
179
(v)
Age (in years)
Cumulative Frequency
20 - 30
52
30 - 40
89
40 - 50
143
50 - 60
179
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 - 240
241 - 281
282 - 322
323 - 363
364 - 404
405 - 445
Labourers
9
7
19
2
7
1
(i)
Wages (in rupees)
Cumulative Frequency
200 - 240
9
241 - 281
10
282 - 322
29
323 - 363
31
364 - 404
38
405 - 445
45
(ii)
Wages (in rupees)
Cumulative Frequency
200 - 240
9
241 - 281
16
282 - 322
35
323 - 363
37
364 - 404
44
405 - 445
45
(iii)
Wages (in rupees)
Cumulative Frequency
200 - 240
9
241 - 281
16
282 - 322
35
323 - 363
39
364 - 404
46
405 - 445
47
(iv)
Wages (in rupees)
Cumulative Frequency
200 - 240
9
241 - 281
28
282 - 322
35
323 - 363
37
364 - 404
44
405 - 445
45
(v)
Wages (in rupees)
Cumulative Frequency
200 - 240
9
241 - 281
16
282 - 322
32
323 - 363
34
364 - 404
41
405 - 445
42
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 - 340
340 - 380
380 - 420
420 - 460
460 - 500
500 - 540
Labourers
1
5
16
11
10
15
(i)
Wages (in rupees)
Cumulative Frequency
300 - 340
1
340 - 380
6
380 - 420
17
420 - 460
28
460 - 500
38
500 - 540
53
(ii)
Wages (in rupees)
Cumulative Frequency
300 - 340
1
340 - 380
16
380 - 420
32
420 - 460
43
460 - 500
53
500 - 540
58
(iii)
Wages (in rupees)
Cumulative Frequency
300 - 340
1
340 - 380
17
380 - 420
22
420 - 460
33
460 - 500
43
500 - 540
58
(iv)
Wages (in rupees)
Cumulative Frequency
300 - 340
1
340 - 380
6
380 - 420
22
420 - 460
35
460 - 500
45
500 - 540
60
(v)
Wages (in rupees)
Cumulative Frequency
300 - 340
1
340 - 380
6
380 - 420
22
420 - 460
33
460 - 500
43
500 - 540
58
Question
7
7.
Identify the cumulative frequency of the given grouped data.
class interval
20 - 30
31 - 41
42 - 52
53 - 63
64 - 74
frequency
17
25
25
15
14
(i)
class interval
Cumulative Frequency
20 - 30
17
31 - 41
31
42 - 52
56
53 - 63
71
64 - 74
96
(ii)
class interval
Cumulative Frequency
20 - 30
17
31 - 41
42
42 - 52
63
53 - 63
78
64 - 74
92
(iii)
class interval
Cumulative Frequency
20 - 30
17
31 - 41
42
42 - 52
67
53 - 63
82
64 - 74
96
(iv)
class interval
Cumulative Frequency
20 - 30
17
31 - 41
39
42 - 52
64
53 - 63
79
64 - 74
93
Question
8
8.
Identify the cumulative frequency of the given grouped data.
class interval
23 - 31
31 - 39
39 - 47
47 - 55
55 - 63
63 - 71
frequency
25
25
11
16
15
25
(i)
class interval
Cumulative Frequency
23 - 31
25
31 - 39
50
39 - 47
61
47 - 55
77
55 - 63
92
63 - 71
117
(ii)
class interval
Cumulative Frequency
23 - 31
25
31 - 39
50
39 - 47
61
47 - 55
73
55 - 63
88
63 - 71
113
(iii)
class interval
Cumulative Frequency
23 - 31
25
31 - 39
50
39 - 47
57
47 - 55
73
55 - 63
88
63 - 71
113
(iv)
class interval
Cumulative Frequency
23 - 31
25
31 - 39
36
39 - 47
61
47 - 55
77
55 - 63
92
63 - 71
117
Question
9
9.
Less than cumulative curves are drawn using
(i)
lower boundaries of classes and less than cumulative frequencies
(ii)
upper boundaries of classes and less than cumulative frequencies
(iii)
lower boundaries of classes and greater 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)
mid values of classes and greater than cumulative frequencies
(iii)
upper boundaries of classes and less than cumulative frequencies
(iv)
lower boundaries of classes and greater than cumulative frequencies
Question
11
11.
Find the cumulative frequency of class
60
-
68
.
Class-Interval
33 - 41
42 - 50
51 - 59
60 - 68
69 - 77
78 - 86
Frequency
20
22
11
17
11
18
(i)
69
(ii)
70
(iii)
71
(iv)
72
(v)
67
Question
12
12.
Find the cumulative frequency of class
56
-
65
.
Class-Interval
11 - 20
20 - 29
29 - 38
38 - 47
47 - 56
56 - 65
Frequency
8
22
7
25
16
15
(i)
94
(ii)
93
(iii)
92
(iv)
95
(v)
90
Question
13
13.
The following cumulative frequency table represents which of the following frequency distribution
Class-Interval
Cumulative Frequency
40 - 45
15
45 - 50
23
50 - 55
31
55 - 60
47
60 - 65
57
65 - 70
73
(i)
Class-Interval
40 - 45
45 - 50
50 - 55
55 - 60
60 - 65
65 - 70
Frequency
15
16
8
16
10
8
(ii)
Class-Interval
40 - 45
45 - 50
50 - 55
55 - 60
60 - 65
65 - 70
Frequency
15
8
8
16
10
16
(iii)
Class-Interval
40 - 45
45 - 50
50 - 55
55 - 60
60 - 65
65 - 70
Frequency
15
8
8
18
10
16
(iv)
Class-Interval
40 - 45
45 - 50
50 - 55
55 - 60
60 - 65
65 - 70
Frequency
15
8
3
16
10
16
Question
14
14.
The following cumulative frequency table represents which of the following frequency distribution
Class-Interval
Cumulative Frequency
35 - 41
52
41 - 47
42
47 - 53
35
53 - 59
23
59 - 65
14
(i)
Class-Interval
35 - 41
41 - 47
47 - 53
53 - 59
59 - 65
Frequency
10
10
12
9
14
(ii)
Class-Interval
35 - 41
41 - 47
47 - 53
53 - 59
59 - 65
Frequency
10
7
14
9
14
(iii)
Class-Interval
35 - 41
41 - 47
47 - 53
53 - 59
59 - 65
Frequency
10
12
7
9
14
(iv)
Class-Interval
35 - 41
41 - 47
47 - 53
53 - 59
59 - 65
Frequency
10
7
12
9
14
(v)
Class-Interval
35 - 41
41 - 47
47 - 53
53 - 59
59 - 65
Frequency
10
14
12
9
7
Question
15
15.
During the medical check-up of 58 students of a class, their weights in kgs are recorded as follows.
Identify the number of students whose weight is more than 40 kg
Class-Interval
35 - 40
40 - 45
45 - 50
50 - 55
55 - 60
60 - 65
Frequency
12
11
6
11
9
9
(i)
45
(ii)
47
(iii)
44
(iv)
48
(v)
46
Assignment Key
1) (iii)
2) (iii)
3) (iii)
4) (v)
5) (ii)
6) (v)
7) (iii)
8) (i)
9) (ii)
10) (iv)
11) (ii)
12) (ii)
13) (ii)
14) (iv)
15) (v)
