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(i) The number of students in a class.
(ii) The number of books in a library.
(iii) Toys sold on a particular day at a shop.
(iv) People who voted for a particular candidate.
(v) Runs scored by a batsman on each ball in a particular evening.
All of the data in Q.1 is primary data.

Five examples of data that we can collect in our daily life are
(i) Number of students in a class.
(ii) The number of books in a library.
(iii) Toys sold on a particular day at a shop.
(iv) People who voted for a particular candidate.
(v) Runs scored by a batsman on each ball in a particular evening.

Production yield
(Upper-Class Limit)
Cumulative
Frequency
More than or equal to 50
100
More than or equal to 55
98
More than or equal to 60
90
More than or equal to 65
78
More than or equal to 70
54
More than or equal to 75
16
Now,
Taking lower class limit on the x-axis and their respective frequencies on the y-axis,

Taking upper-class interval on the x-axis and their respective frequencies on the y-axis,
Marking a point on the curve whose ordinate is 17.5 gives an x-ordinate= 46.5.
Hence, the Median of the data is 46.5
Now,
Weight
(Class)
Frequency
Cumulative
Frequency
>38
0
0
38-40
3
3
40-42
2
5
42-44
4
9
44-46
5
14
46-48
14
28
48-50
4
32
50-52
3
35
Median class = 46-48;...

Daily Income
(Upper Class Limit)
Cumulative
Frequency
Less than 120
12
Less than 140
26
Less than 160
34
Less than 180
40
Less than 200
50
Now,
Taking upper class interval on x-axis and their respective frequencies on y-axis,

Class
Number of
students
Cumulative
Frequency
40-45
2
2
45-50
3
5
50-55
8
13
55-60
6
19
60-65
6
25
65-70
3
28
70-75
2
30
MEDIAN:
Median class = 55-60; Lower limit, l = 55;
Cumulative frequency of preceding class, c.f. = 13; f = 6; h = 5
Thus, median weight of the student is 56.67 kg

Class
Number of
surnames
Cumulative
Frequency
Class mark
1-4
6
6
2.5
15
4-7
30
36
5.5
165
7-10
40
76
8.5
340
10-13
16
92
11.5
184
13-16
4
96
14.5
51
16-19
4
100
17.5
70
= 100
= 825
MEDIAN:
Median class = 7-10; Lower limit, l = 7;
Cumulative frequency of preceding class, c.f. = 36; f = 40; h = 3
Thus, the median of the data is 8.05
MODE:
The...

Class
Frequency
Cumulative
Frequency
1500-2000
14
14
2000-2500
56
70
2500-3000
60
130
3000-3500
86
216
3500-4000
74
290
4000-4500
62
352
4500-5000
48
400
Therefore, Median class = 3000-3500
Lower limit, l = 3000; Class height, h = 500
Frequency corresponding to median class, f = 86
Cumulative frequency of the class preceding the median class, c.f. =...

The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes.
Class
Frequency
Cumulative
Frequency
117.5-126.5
3
3
126.5-135.5
5
8
135.5-144.5
9
17
144.5-153.5
12
29
153.5-162.5
5
34
162.5-171.5
4
38
171.5-180.5
2
40
Therefore, Median class = 144.5-153.5
Lower limit, l = 144.5; Class height, h =...

Class
Frequency
Cumulative
Frequency
15-20
2
2
20-25
4
6
25-30
18
24
30-35
21
45
35-40
33
78
40-45
11
89
45-50
3
92
50-55
6
98
55-60
2
100
Therefore, Median class = 35-45
Frequency corresponding to median class, f = 21
Cumulative frequency of the class preceding the median class, c.f. = 24
Lower limit, l = 35; Class height, h = 10
Thus, median age is 35.75 years.

Class
Number of
consumers
Cumulative
Frequency
0-10
5
5
10-20
x
5+x
20-30
20
25+x
30-40
15
40+x
40-50
y
40+x+y
50-60
5
45+x+y
= 60
Now,
Given median = 28.5 which lies in the class 20-30
Therefore, Median class = 20-30
Frequency corresponding to median class, f = 20
Cumulative frequency of the class preceding the median class, c.f. = 5 + x
Lower limit, l...

Let the assumed mean be a = 130 and h = 20
Class
Number of
consumers
Cumulative
Frequency
Class mark
65-85
4
4
70
-60
-3
-12
85-105
5
9
90
-40
-2
-10
105-125
13
22
110
-20
-1
-13
125-145
20
42
130
0
0
0
145-165
14
56
150
20
1
14
165-185
8
64
170
40
2
16
185-205
4
68
190
60
3
12
= 68
= 7
MEDIAN:
Median class = 125-145; Cumulative Frequency...

The class having maximum frequency is the modal class.
The maximum frequency is 20 and hence the modal class = 40-50
Lower limit (l) of modal class = 40, class size (h) = 10
Frequency ( ) of the modal class = 20 frequency ( ) of class preceding the modal class = 12, frequency ( ) of class succeeding the modal class = 11
Thus, Mode of the data is 44.70

The class having maximum frequency is the modal class.
The maximum frequency is 18 and hence the modal class = 4000-5000
Lower limit (l) of modal class = 4000, class size (h) = 1000
Frequency ( ) of the modal class = 18 frequency ( ) of class preceding the modal class = 4, frequency ( ) of class succeeding the modal class = 9
Thus, Mode of the data is 4608.70

The class having maximum frequency is the modal class.
The maximum frequency is 10 and hence the modal class = 30-35
Lower limit (l) of modal class = 30, class size (h) = 5
Frequency ( ) of the modal class = 10 frequency ( ) of class preceding the modal class = 9, frequency ( ) of class succeeding the modal class = 3
Thus, Mode of the data is 30.625
Now,
Let the assumed mean be a =...

The class having maximum frequency is the modal class.
The maximum frequency is 40 and hence the modal class = 1500-2000
Lower limit (l) of modal class = 1500, class size (h) = 500
Frequency ( ) of the modal class = 40 frequency ( ) of class preceding the modal class = 24, frequency ( ) of class succeeding the modal class = 33.
Thus, Mode of the data is Rs. 1847.82
Now,
Let the assumed...

The class having maximum frequency is the modal class.
The maximum frequency is 61 and hence the modal class = 60-80
Lower limit (l) of modal class = 60, class size (h) = 20
Frequency ( ) of the modal class = 61 frequency ( ) of class preceding the modal class = 52, frequency ( ) of class succeeding the modal class = 38.
Thus, the modal lifetime of 225 electrical components is 65.62 hours

The class having maximum frequency is the modal class.
The maximum frequency is 23 and hence the modal class = 35-45
Lower limit (l) of modal class = 35, class size (h) = 10
Frequency ( ) of the modal class = 23, frequency ( ) of class preceding the modal class = 21, frequency ( ) of class succeeding the modal class = 14.
Now,
Age
Number of
patients
Class...

Let the assumed mean be a = 75 and h = 10
Literacy
rates
Number of
cities
Class mark
45-55
3
50
-20
-2
-6
55-65
10
60
-10
-1
-10
65-75
11
70
0
0
0
75-85
8
80
10
1
8
85-95
3
90
20
2
6
= 35
= -2
Mean,
Therefore, the mean mean literacy rate is 69.43%

Number of
days
Number of
Students
Class mark
0-6
11
3
33
6-10
10
8
80
10-14
7
12
84
14-20
4
17
68
20-28
4
24
96
28-38
3
33
99
38-40
1
39
39
=40
=499
Mean,
Therefore, the mean number of days a student was absent is 12.48 days.

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