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
28 - 36
12
37 - 45
28
46 - 54
38
55 - 63
47
64 - 72
53
73 - 81
63
82 - 90
74
91 - 99
90
(i)
Class-Interval
28 - 36
37 - 45
46 - 54
55 - 63
64 - 72
73 - 81
82 - 90
91 - 99
Frequency
12
16
15
9
6
10
11
16
(ii)
Class-Interval
28 - 36
37 - 45
46 - 54
55 - 63
64 - 72
73 - 81
82 - 90
91 - 99
Frequency
12
16
9
10
6
10
11
16
(iii)
Class-Interval
28 - 36
37 - 45
46 - 54
55 - 63
64 - 72
73 - 81
82 - 90
91 - 99
Frequency
12
16
10
9
11
10
11
16
(iv)
Class-Interval
28 - 36
37 - 45
46 - 54
55 - 63
64 - 72
73 - 81
82 - 90
91 - 99
Frequency
12
16
10
9
6
10
11
16
Question
2
2.
Construct a frequency distribution table from the following cumulative frequency distribution
Class-Interval
Cumulative Frequency
19 - 27
13
27 - 35
28
35 - 43
33
43 - 51
39
51 - 59
50
59 - 67
62
67 - 75
67
(i)
Class-Interval
19 - 27
27 - 35
35 - 43
43 - 51
51 - 59
59 - 67
67 - 75
Frequency
13
15
5
9
11
12
5
(ii)
Class-Interval
19 - 27
27 - 35
35 - 43
43 - 51
51 - 59
59 - 67
67 - 75
Frequency
13
15
5
6
11
12
5
(iii)
Class-Interval
19 - 27
27 - 35
35 - 43
43 - 51
51 - 59
59 - 67
67 - 75
Frequency
13
15
10
6
11
12
5
(iv)
Class-Interval
19 - 27
27 - 35
35 - 43
43 - 51
51 - 59
59 - 67
67 - 75
Frequency
13
5
15
6
11
12
5
(v)
Class-Interval
19 - 27
27 - 35
35 - 43
43 - 51
51 - 59
59 - 67
67 - 75
Frequency
13
5
5
6
11
12
15
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
No. of Patients
81
86
67
45
88
76
(i)
Age (in years)
Cumulative Frequency
10 - 20
81
21 - 31
167
32 - 42
234
43 - 53
279
54 - 64
367
65 - 75
443
(ii)
Age (in years)
Cumulative Frequency
10 - 20
81
21 - 31
167
32 - 42
234
43 - 53
281
54 - 64
369
65 - 75
445
(iii)
Age (in years)
Cumulative Frequency
10 - 20
81
21 - 31
148
32 - 42
234
43 - 53
279
54 - 64
367
65 - 75
443
(iv)
Age (in years)
Cumulative Frequency
10 - 20
81
21 - 31
157
32 - 42
224
43 - 53
269
54 - 64
357
65 - 75
443
(v)
Age (in years)
Cumulative Frequency
10 - 20
81
21 - 31
167
32 - 42
231
43 - 53
276
54 - 64
364
65 - 75
440
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
60 - 70
70 - 80
80 - 90
90 - 100
No. of Patients
20
31
77
68
60
43
56
34
(i)
Age (in years)
Cumulative Frequency
20 - 30
20
30 - 40
51
40 - 50
128
50 - 60
196
60 - 70
258
70 - 80
301
80 - 90
357
90 - 100
391
(ii)
Age (in years)
Cumulative Frequency
20 - 30
20
30 - 40
51
40 - 50
119
50 - 60
196
60 - 70
256
70 - 80
299
80 - 90
355
90 - 100
389
(iii)
Age (in years)
Cumulative Frequency
20 - 30
20
30 - 40
51
40 - 50
128
50 - 60
196
60 - 70
256
70 - 80
299
80 - 90
355
90 - 100
389
(iv)
Age (in years)
Cumulative Frequency
20 - 30
20
30 - 40
51
40 - 50
132
50 - 60
200
60 - 70
260
70 - 80
303
80 - 90
359
90 - 100
393
(v)
Age (in years)
Cumulative Frequency
20 - 30
20
30 - 40
54
40 - 50
131
50 - 60
199
60 - 70
259
70 - 80
302
80 - 90
358
90 - 100
389
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
14
5
20
20
19
4
(i)
Wages (in rupees)
Cumulative Frequency
200 - 230
14
231 - 261
34
262 - 292
39
293 - 323
59
324 - 354
78
355 - 385
82
(ii)
Wages (in rupees)
Cumulative Frequency
200 - 230
14
231 - 261
18
262 - 292
38
293 - 323
58
324 - 354
77
355 - 385
82
(iii)
Wages (in rupees)
Cumulative Frequency
200 - 230
14
231 - 261
19
262 - 292
39
293 - 323
59
324 - 354
78
355 - 385
82
(iv)
Wages (in rupees)
Cumulative Frequency
200 - 230
14
231 - 261
19
262 - 292
36
293 - 323
56
324 - 354
75
355 - 385
79
(v)
Wages (in rupees)
Cumulative Frequency
200 - 230
14
231 - 261
19
262 - 292
39
293 - 323
61
324 - 354
80
355 - 385
84
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
9
16
1
1
15
3
(i)
Wages (in rupees)
Cumulative Frequency
300 - 340
9
340 - 380
10
380 - 420
26
420 - 460
27
460 - 500
42
500 - 540
45
(ii)
Wages (in rupees)
Cumulative Frequency
300 - 340
9
340 - 380
25
380 - 420
26
420 - 460
27
460 - 500
42
500 - 540
45
(iii)
Wages (in rupees)
Cumulative Frequency
300 - 340
9
340 - 380
25
380 - 420
29
420 - 460
30
460 - 500
45
500 - 540
48
(iv)
Wages (in rupees)
Cumulative Frequency
300 - 340
9
340 - 380
12
380 - 420
13
420 - 460
14
460 - 500
29
500 - 540
45
(v)
Wages (in rupees)
Cumulative Frequency
300 - 340
9
340 - 380
25
380 - 420
26
420 - 460
29
460 - 500
44
500 - 540
47
Question
7
7.
Identify the cumulative frequency of the given grouped data.
class interval
13 - 23
24 - 34
35 - 45
46 - 56
57 - 67
frequency
11
5
9
11
16
(i)
class interval
Cumulative Frequency
13 - 23
11
24 - 34
12
35 - 45
21
46 - 56
32
57 - 67
48
(ii)
class interval
Cumulative Frequency
13 - 23
11
24 - 34
27
35 - 45
36
46 - 56
47
57 - 67
52
(iii)
class interval
Cumulative Frequency
13 - 23
11
24 - 34
16
35 - 45
27
46 - 56
38
57 - 67
54
(iv)
class interval
Cumulative Frequency
13 - 23
11
24 - 34
16
35 - 45
25
46 - 56
36
57 - 67
52
(v)
class interval
Cumulative Frequency
13 - 23
11
24 - 34
20
35 - 45
25
46 - 56
36
57 - 67
52
Question
8
8.
Identify the cumulative frequency of the given grouped data.
class interval
15 - 21
21 - 27
27 - 33
33 - 39
frequency
23
8
25
12
(i)
class interval
Cumulative Frequency
15 - 21
23
21 - 27
31
27 - 33
52
33 - 39
64
(ii)
class interval
Cumulative Frequency
15 - 21
23
21 - 27
48
27 - 33
56
33 - 39
68
(iii)
class interval
Cumulative Frequency
15 - 21
23
21 - 27
31
27 - 33
56
33 - 39
68
(iv)
class interval
Cumulative Frequency
15 - 21
23
21 - 27
29
27 - 33
54
33 - 39
66
(v)
class interval
Cumulative Frequency
15 - 21
12
21 - 27
20
27 - 33
45
33 - 39
68
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)
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)
lower 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
48
-
53
.
Class-Interval
24 - 29
30 - 35
36 - 41
42 - 47
48 - 53
54 - 59
60 - 65
Frequency
13
18
7
10
23
13
8
(i)
70
(ii)
73
(iii)
71
(iv)
69
(v)
72
Question
12
12.
Find the cumulative frequency of class
49
-
57
.
Class-Interval
41 - 49
49 - 57
57 - 65
65 - 73
Frequency
5
6
23
23
(i)
12
(ii)
10
(iii)
11
(iv)
14
(v)
8
Question
13
13.
The following cumulative frequency table represents which of the following frequency distribution
Class-Interval
Cumulative Frequency
40 - 49
15
49 - 58
27
58 - 67
32
67 - 76
40
76 - 85
49
(i)
Class-Interval
40 - 49
49 - 58
58 - 67
67 - 76
76 - 85
Frequency
15
12
8
8
9
(ii)
Class-Interval
40 - 49
49 - 58
58 - 67
67 - 76
76 - 85
Frequency
15
12
5
8
9
(iii)
Class-Interval
40 - 49
49 - 58
58 - 67
67 - 76
76 - 85
Frequency
15
9
5
8
9
(iv)
Class-Interval
40 - 49
49 - 58
58 - 67
67 - 76
76 - 85
Frequency
15
9
5
8
12
(v)
Class-Interval
40 - 49
49 - 58
58 - 67
67 - 76
76 - 85
Frequency
15
5
12
8
9
Question
14
14.
The following cumulative frequency table represents which of the following frequency distribution
Class-Interval
Cumulative Frequency
33 - 41
58
41 - 49
53
49 - 57
42
57 - 65
31
65 - 73
20
73 - 81
14
81 - 89
5
(i)
Class-Interval
33 - 41
41 - 49
49 - 57
57 - 65
65 - 73
73 - 81
81 - 89
Frequency
5
11
11
11
6
9
5
(ii)
Class-Interval
33 - 41
41 - 49
49 - 57
57 - 65
65 - 73
73 - 81
81 - 89
Frequency
5
5
11
11
6
9
11
(iii)
Class-Interval
33 - 41
41 - 49
49 - 57
57 - 65
65 - 73
73 - 81
81 - 89
Frequency
5
11
6
11
6
9
5
(iv)
Class-Interval
33 - 41
41 - 49
49 - 57
57 - 65
65 - 73
73 - 81
81 - 89
Frequency
5
11
11
7
6
9
5
Question
15
15.
During the medical check-up of 67 students of a class, their weights in kgs are recorded as follows.
Identify the number of students whose weight is more than 86 kg
Class-Interval
30 - 38
38 - 46
46 - 54
54 - 62
62 - 70
70 - 78
78 - 86
86 - 94
Frequency
5
11
6
7
10
8
11
9
(i)
12
(ii)
8
(iii)
9
(iv)
10
(v)
6
Assignment Key
1) (iv)
2) (ii)
3) (i)
4) (iii)
5) (iii)
6) (ii)
7) (iv)
8) (iii)
9) (i)
10) (iii)
11) (iii)
12) (iii)
13) (ii)
14) (i)
15) (iii)
