EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Frequency Distribution
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
If the lower and upper limit of class interval are 19 and 22 respectively, then the class interval is
(i)
19
-
22.5
(ii)
19.5
-
21.5
(iii)
18.5
-
22.5
(iv)
18.5
-
22
(v)
19
-
22
Question
2
2.
In inclusive form representation, the observation
54
falls in which class?
(i)
34
-
44
(ii)
39
-
49
(iii)
55
-
64
(iv)
43
-
53
(v)
44
-
54
Question
3
3.
The weights (in gm) of
20
fruits are as follows.
Form the grouped frequency table
in inclusive form
by taking class size
40
.
276
251
268
305
265
251
281
266
214
329
296
364
235
212
383
279
268
323
272
310
(i)
Weight (in gm)
212 - 251
252 - 291
292 - 331
332 - 371
372 - 411
No. of Fruits
5
8
3
1
1
(ii)
Weight (in gm)
212 - 251
252 - 291
292 - 331
332 - 371
372 - 411
No. of Fruits
5
8
5
1
1
(iii)
Weight (in gm)
212 - 251
252 - 291
292 - 331
332 - 371
372 - 411
No. of Fruits
5
1
5
1
8
(iv)
Weight (in gm)
212 - 251
252 - 291
292 - 331
332 - 371
372 - 411
No. of Fruits
5
6
5
1
1
(v)
Weight (in gm)
212 - 251
252 - 291
292 - 331
332 - 371
372 - 411
No. of Fruits
5
5
8
1
1
Question
4
4.
If the sum of the following frequency distribution is
33
,
find the value of 'x'.
Class-Interval
Frequency
10 - 20
4
21 - 31
7
32 - 42
x
43 - 53
9
54 - 64
10
(i)
5
(ii)
3
(iii)
4
(iv)
2
(v)
0
Question
5
5.
Which of the following are discontinuous variables?
a)
Heights of children in a class.
b)
Number of workers in a factory.
c)
Wages of workers in a factory.
d)
Number of members in a family.
e)
Weights of persons in a group.
(i)
{c,d}
(ii)
{a,b}
(iii)
{c,d,b}
(iv)
{b,d}
(v)
{e,a,b}
Question
6
6.
The daily wages (in rupees) of
17
workers in a factory are given below.
Represent the data in the form of a frequency distribution
in exclusive form
taking class size
20
.
248
275
276
240
267
229
224
236
224
268
209
250
292
259
250
224
250
(i)
Wages (in rupees)
209 - 229
229 - 249
249 - 269
269 - 289
289 - 309
No. of Workers
4
4
6
2
1
(ii)
Wages (in rupees)
209 - 229
229 - 249
249 - 269
269 - 289
289 - 309
No. of Workers
4
6
4
2
1
(iii)
Wages (in rupees)
209 - 229
229 - 249
249 - 269
269 - 289
289 - 309
No. of Workers
4
7
6
2
1
(iv)
Wages (in rupees)
209 - 229
229 - 249
249 - 269
269 - 289
289 - 309
No. of Workers
4
1
6
2
4
(v)
Wages (in rupees)
209 - 229
229 - 249
249 - 269
269 - 289
289 - 309
No. of Workers
4
4
9
2
1
Question
7
7.
Find the cumulative frequency of class
25
-
30
.
Class-Interval
19 - 24
25 - 30
31 - 36
37 - 42
43 - 48
49 - 54
55 - 60
61 - 66
Frequency
15
18
23
5
22
23
10
6
(i)
33
(ii)
31
(iii)
36
(iv)
32
(v)
34
Question
8
8.
The marks obtained by
17
students in an examination are given below.
Represent the data in the form of a frequency distribution table
in exclusive form
taking class size
5
.
47
42
75
46
42
73
65
44
64
73
71
56
62
73
54
80
55
(i)
Marks
42 - 47
47 - 52
52 - 57
57 - 62
62 - 67
67 - 72
72 - 77
77 - 82
No. of Students
4
1
0
3
3
1
4
1
(ii)
Marks
42 - 47
47 - 52
52 - 57
57 - 62
62 - 67
67 - 72
72 - 77
77 - 82
No. of Students
4
1
3
0
7
1
4
1
(iii)
Marks
42 - 47
47 - 52
52 - 57
57 - 62
62 - 67
67 - 72
72 - 77
77 - 82
No. of Students
4
1
3
0
3
1
4
1
(iv)
Marks
42 - 47
47 - 52
52 - 57
57 - 62
62 - 67
67 - 72
72 - 77
77 - 82
No. of Students
4
1
6
0
3
1
4
1
Question
9
9.
The class mark of the class with frequency x is
Class-Interval
Frequency
12 - 22
15
22 - 32
x
32 - 42
13
42 - 52
9
52 - 62
6
(i)
24
(ii)
26
(iii)
28
(iv)
30
(v)
27
Question
10
10.
The class boundaries of 22 - 28 which is in inclusive form are
(i)
21
-
29
(ii)
21.5
-
28.5
(iii)
21
-
28.5
(iv)
22
-
28
(v)
21.5
-
29
Question
11
11.
The class boundaries of 49 - 51 which is in exclusive form are
(i)
49
-
51.5
(ii)
49
-
51
(iii)
49.5
-
50.5
(iv)
48.5
-
51
(v)
48.5
-
51.5
Question
12
12.
During the medical check-up of 49 students of a class, their weights in kgs are recorded as follows.
Identify the number of students whose weight is less than 60 kg
Class-Interval
33 - 42
42 - 51
51 - 60
60 - 69
69 - 78
78 - 87
Frequency
7
9
9
8
7
9
(i)
24
(ii)
22
(iii)
26
(iv)
25
(v)
28
Question
13
13.
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
No. of Patients
52
78
59
90
65
(i)
Age (in years)
Cumulative Frequency
20 - 30
52
30 - 40
111
40 - 50
189
50 - 60
279
60 - 70
344
(ii)
Age (in years)
Cumulative Frequency
20 - 30
52
30 - 40
130
40 - 50
186
50 - 60
276
60 - 70
341
(iii)
Age (in years)
Cumulative Frequency
20 - 30
52
30 - 40
117
40 - 50
176
50 - 60
266
60 - 70
344
(iv)
Age (in years)
Cumulative Frequency
20 - 30
52
30 - 40
130
40 - 50
189
50 - 60
279
60 - 70
344
(v)
Age (in years)
Cumulative Frequency
20 - 30
52
30 - 40
125
40 - 50
184
50 - 60
274
60 - 70
339
Question
14
14.
If the sum of the following frequency distribution is
39
,
find the value of 'x'.
Value
Frequency
4
5
5
x
6
4
7
3
8
4
9
3
10
3
11
6
12
3
13
5
(i)
4
(ii)
2
(iii)
3
(iv)
5
(v)
1
Question
15
15.
Which of the following class intervals are in exclusive form?
a)
28 - 33 , 33 - 38 , 38 - 43...
b)
13 - 18 , 18 - 23 , 23 - 28,...
c)
12.5 - 18.5 , 18.5 - 24.5 , 24.5 - 30.5...
d)
13 - 18 , 19 - 24 , 25 - 30,...
e)
31 - 36 , 37 - 42 , 43 - 48,...
(i)
{e,b}
(ii)
{a,b,c}
(iii)
{d,a}
(iv)
{d,e,c}
(v)
{d,a,b}
Question
16
16.
Find the sum of frequencies for the given table
Value
15
16
26
46
47
53
61
63
69
73
Frequency
1
1
1
1
1
1
1
1
1
1
(i)
9
(ii)
11
(iii)
12
(iv)
8
(v)
10
Question
17
17.
The class boundaries of the class with frequency x is
Class-Interval
Frequency
27 - 32
27
33 - 38
22
39 - 44
4
45 - 50
13
51 - 56
x
(i)
50
-
57
(ii)
50
-
56.5
(iii)
51
-
56
(iv)
50.5
-
57
(v)
50.5
-
56.5
Question
18
18.
The class mark of the class with frequency x is
Class-Interval
Frequency
13 - 18
25
19 - 24
2
25 - 30
x
31 - 36
16
37 - 42
16
(i)
55
2
(ii)
109
4
(iii)
53
2
(iv)
28
(v)
57
2
Question
19
19.
The class boundaries of the class with frequency x is
Class-Interval
Frequency
48 - 53
22
53 - 58
14
58 - 63
17
63 - 68
26
68 - 73
x
(i)
68
-
73
(ii)
67.5
-
73
(iii)
68
-
73.5
(iv)
68.5
-
72.5
(v)
67.5
-
73.5
Question
20
20.
The number of children in 19 families are given below. Identify the frequency distribution table for the given data.
0
0
4
0
0
5
5
1
5
3
4
1
3
1
4
0
3
1
0
(i)
No. of children
0
1
2
3
4
5
No. of families
1
1
2
5
6
4
(ii)
No. of children
0
2
3
4
5
No. of families
4
5
2
4
4
(iii)
No. of children
0
1
3
4
5
No. of families
6
4
3
3
3
Question
21
21.
Identify the frequency distribution table for the given heights of 14 students in cm
177
151
166
156
175
171
167
154
168
171
169
158
167
177
(i)
Height (in cm)
151
155
156
157
159
164
167
168
169
175
No. of Students
2
4
1
1
1
1
1
1
1
1
(ii)
Height (in cm)
151
154
158
166
167
168
169
171
175
177
No. of Students
1
1
1
1
3
1
1
2
1
2
(iii)
Height (in cm)
151
154
156
158
166
167
168
169
171
175
177
No. of Students
1
1
1
1
1
3
1
1
2
1
1
(iv)
Height (in cm)
150
153
154
156
162
164
169
171
173
174
180
No. of Students
1
1
1
1
3
1
1
2
1
1
1
(v)
Height (in cm)
151
154
156
158
166
167
168
169
171
175
177
No. of Students
1
1
1
1
1
2
1
1
2
1
2
Question
22
22.
Construct a frequency distribution table from the following cumulative frequency distribution
Class-Interval
Cumulative Frequency
11 - 16
11
17 - 22
26
23 - 28
32
29 - 34
46
35 - 40
56
41 - 46
72
(i)
Class-Interval
11 - 16
17 - 22
23 - 28
29 - 34
35 - 40
41 - 46
Frequency
11
6
15
14
10
16
(ii)
Class-Interval
11 - 16
17 - 22
23 - 28
29 - 34
35 - 40
41 - 46
Frequency
11
16
6
14
10
15
(iii)
Class-Interval
11 - 16
17 - 22
23 - 28
29 - 34
35 - 40
41 - 46
Frequency
11
15
6
19
10
16
(iv)
Class-Interval
11 - 16
17 - 22
23 - 28
29 - 34
35 - 40
41 - 46
Frequency
11
15
2
14
10
16
(v)
Class-Interval
11 - 16
17 - 22
23 - 28
29 - 34
35 - 40
41 - 46
Frequency
11
15
6
14
10
16
Question
23
23.
Identify the cumulative frequency of the given grouped data.
class interval
10 - 19
20 - 29
30 - 39
40 - 49
50 - 59
60 - 69
70 - 79
frequency
13
18
17
7
6
13
13
(i)
class interval
Cumulative Frequency
10 - 19
13
20 - 29
31
30 - 39
48
40 - 49
50
50 - 59
56
60 - 69
69
70 - 79
82
(ii)
class interval
Cumulative Frequency
10 - 19
13
20 - 29
31
30 - 39
45
40 - 49
52
50 - 59
58
60 - 69
71
70 - 79
84
(iii)
class interval
Cumulative Frequency
10 - 19
13
20 - 29
30
30 - 39
48
40 - 49
55
50 - 59
61
60 - 69
74
70 - 79
87
(iv)
class interval
Cumulative Frequency
10 - 19
13
20 - 29
26
30 - 39
43
40 - 49
50
50 - 59
56
60 - 69
69
70 - 79
87
(v)
class interval
Cumulative Frequency
10 - 19
13
20 - 29
31
30 - 39
48
40 - 49
55
50 - 59
61
60 - 69
74
70 - 79
87
Question
24
24.
The true lower limit and true upper limit of the class with frequency x is
Class-Interval
Frequency
10 - 15
12
16 - 21
13
22 - 27
x
28 - 33
30
34 - 39
8
(i)
22
-
27
(ii)
21.5
-
27.5
(iii)
21
-
27.5
(iv)
21
-
28
(v)
21.5
-
28
Question
25
25.
The marks obtained by
19
students in an examination are given below.
Represent the data in the form of a frequency distribution table
in exclusive form
taking class size
6
.
66
77
48
67
46
51
41
46
67
70
44
49
63
53
41
52
75
78
76
(i)
Marks
41 - 47
47 - 53
53 - 59
59 - 65
65 - 71
71 - 77
77 - 83
No. of Students
5
2
1
1
4
2
4
(ii)
Marks
41 - 47
47 - 53
53 - 59
59 - 65
65 - 71
71 - 77
77 - 83
No. of Students
5
4
1
1
4
2
2
(iii)
Marks
41 - 47
47 - 53
53 - 59
59 - 65
65 - 71
71 - 77
77 - 83
No. of Students
5
1
4
1
4
2
2
(iv)
Marks
41 - 47
47 - 53
53 - 59
59 - 65
65 - 71
71 - 77
77 - 83
No. of Students
5
4
1
5
4
2
2
(v)
Marks
41 - 47
47 - 53
53 - 59
59 - 65
65 - 71
71 - 77
77 - 83
No. of Students
5
4
6
1
4
2
2
Assignment Key
1) (v)
2) (v)
3) (ii)
4) (ii)
5) (iv)
6) (i)
7) (i)
8) (iii)
9) (v)
10) (ii)
11) (ii)
12) (iv)
13) (iv)
14) (iii)
15) (ii)
16) (v)
17) (v)
18) (i)
19) (i)
20) (iii)
21) (v)
22) (v)
23) (v)
24) (ii)
25) (ii)
