5. Calculate average of the following discrete series. Use Short-cut Method by taking 25 as
assumed average.
Size
30
29
28
27
26
25
24
23
22
21
Frequency (f)
2
4
5
3
2
7
1
4.
5
7
Answers
Answer:
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CBSE Class 11-commerce
Tr Jain And Vk Ohri Solutions
Statistics for Economics
Measures of Central Tendency- Arithmetic Mean
TR JAIN AND VK OHRI Solutions for Class 11-commerce Statistics For Economics Chapter 9 - Measures of Central Tendency- Arithmetic Mean
Page / Exercise
176 177 178
Chapter 9 - Measures of Central Tendency- Arithmetic Mean Exercise 176
Question 1
Eight workers earn the following income:
30,36,34,40,42,46,54,62
Find out arithmetic mean.
Solution 1
Question 2
Pocket allowance of 5 students respectively are:
125,75,150,175,200
Find out arithmetic mean.
Solution 2
Question 3
Following is the height of 10 students:
Students
A
B
C
D
E
F
G
H
I
J
Height (cm)
155
153
168
160
162
166
164
180
157
165
Calculate arithmetic mean using Direct and Short-cut Methods.
Solution 3
Question 4
Weight of 15 persons is as follows:
Weigsht (kg)
20
28
34
39
42
50
53
54
59
64
72
74
74
78
79
Find out mean weight, using Direct Method as well as short-cut Method.
Solution 4
Chapter 9 - Measures of Central Tendency- Arithmetic Mean Exercise 177
Question 1
Calculate average of the following discrete series. Use Short-cut Method by taking 25 as assumed average.
Size
30
29
28
27
26
25
24
23
22
21
Frequency (f)
2
4
5
3
2
7
1
4
5
7
Solution 1
Question 2
Marks secured by 42 students in Economics are:
Marks
15
20
22
23
27
35
18
Number of students
8
4
7
3
8
7
5
Find average marks.
Solution 2
Question 3
Average age of the people of a country is shown in the following table:
Age (Years)
10-20
20-30
30-40
40-50
50-60
People ('000)
30
32
15
12
9
Find out mean age by Direct Method.
Solution 3
Question 4
Calculate the arithmetic mean of the following frequency distribution by Direct Method:
Class Interval
10-20
20-40
40-70
70-120
120-200
Frequency
4
10
26
8
2
Solution 4
Question 5
Calculate arithmetic mean from the following data by short-cut Method:
Class Interval
20-25
25-35
30-35
35-40
40-45
45-50
50-55
Frequency
10
12
8
20
11
4
5
Solution 5
Question 6
Find out arithmetic mean from the following distribution by short-cut Method:
Items
10-8
8-6
6-4
4-2
2-0
Frequency
10
8
6
4
2
Solution 6
Question 7
Sachin made the following runs in different matches:
Runs
5-15
15-25
25-35
35-45
45-55
Frequency
10
12
17
19
22
Calculated the average mean of the runs by Step-deviation Method.
Solution 7
Thus, average mean of the runs is 33.875
Question 8
Calculated arithmetic mean of the following frequency distribution:
Class
Less than 10
10-20
20-30
30-40
40-50
50-60
More than 60
Frequency
5
12
18
22
6
4
3
Solution 8
Question 9
Mean marks obtained by a student in his five subject are 15. In English he secures 8 marks, in Economics 12, in Mathematics 18, and in commerce 9. Find out the marks he secured in statistics.
Solution 9
Question 10
Mean value of the weekly income of 40 families is 265. But in the calculation, income of one family was read as 150 instead of 115. Find the "Corrected" mean.
Solution 10
Chapter 9 - Measures of Central Tendency- Arithmetic Mean Exercise 178
Question 1
Average pocket allowance of 6 students is Rs 45. Of these, pocket allowance of 5 students is 20, 30, 22, 24 and 32 respectively. What is the pocket allowance of the sixth student?
Solution 1
Question 2
The following table shows wages of the workers. Calculated the average wage of the workers.
Wages (Rs)
10-19
20-29
30-39
40-49
50-59
Number of workers
8
9
12
11
6
Solution 2
Question 3
Ten player of the Australian team made an average of 63 runs and ten players of the Indian team made an average of 77 runs. Calculated the average run made by both the teams.
Solution 3
Question 4
Average income of 50 families is Rs 3,000. Of these average income of 12 families is Rs 1,800. Find out the average income of the remaining families.
Solution 4
Thus, average income of remaining families is Rs 3378.95.
Question 5
In the following frequency distribution, if the arithmetic mean is 45.6, find out missing frequency.
Wages (Rs)
10-20
20-30
30-40
40-50
50-60
60-70
70-80
Number of workers
5
6
7
X
4
3
9
Solution 5
Thus, missing frequency is 16.
Question 6
Calculate the weighted mean of the following data:
Item
96
102
104
124
148
164
Weight
5
6
3
7
12
9
Solution 6
Question 7
A student obtained 60 marks in English, 75 in Hindi, 63 in Mathematics 59, in Economics and 55 in Statistic. Calculate weight mean of the marks if weight are respectively 2,1,5,5 and 3.
Solution 7
Question 8
A housewife uses 10 kg of Wheat, 20 kg of fuel, 5 kg of Sugar, and 2 kg of oil. Prices (per kg) of these items are Rs 1.50, 150 paise, Rs 2.80 and Rs 10 respectively. Taking quantities used as weight find out the weighted arithmetic average of the prices.
Solution 8
Question 9
Calculate weighted mean of the following data by using Direct and Short-cut Methods:
Items
81
76
74
58
70
73
Weight
2
3
6
7
3
7