2. 2IIM
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Theory
Averages – Basic concepts
2
Average is a measure that gives a general idea about a sample space.
The formula for computing average is straight-forward :
Average =
One basic example
What is the average score in 5 subjects if you score 44, 56, 72, 60 and 28
in them?
Critical skill set - To get average from total, total from average, number of
entities given both.
objectsofnumberTotal
Total
3. 2IIM
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Theory
Averages – Weighted average
Normal average assumes that all measurements have equal weightages.
But we can attach different weights to each measurement as well.
Weighted average formula is as follows.
Average A = , where w1 and w2 are weightages and a1 and
a2 are averages are the respective averages
One basic example
Average weight of 20 boys in a class is 50 kgs. Average weight of 30 girls
in the same class is 40 kgs. What is the overall average weight
Overall average = = 44 kgs.
3
3020
40*3050*20
+
+
21
2211
ww
awaw
+
+
4. 2IIM
Ascent Education’s
An IIM Alumni Venture
Theory
Averages – Standard framework
4
Example question: The average age of the students of a class A comprising
30 students is 16 years and that of class B comprising 20 students is 11
years. What is the average age of the students of the two classes taken
together?
Number * Average = Total
30 16 480
20 11 220
50 = 14 700
50
700
5. 2IIM
Ascent Education’s
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Question
The average revenue of company A in a year was Rs.30,000 a month.
During the first 5 months, the company saw an average revenue of Rs.
25,000 per month and in the last 6 months, the company saw an average
of Rs.33,000 per month. What was the revenue level in the 6th month?
Que:
6. 2IIM
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Solution
The average revenue of company A in a year was Rs.30,000 a month.
During the first 5 months, the company saw an average revenue of Rs.
25,000 per month and in the last 6 months, the company saw an average
of Rs.33,000 per month. What was the revenue level in the 6th month?
Soln:
Number * Average = Total
5 25 k 125 k
1 X X
6 33k 198 k
12 30 360 k
7. 2IIM
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Solution
125k + x + 198k = 360k
x = 37k
Company earns Rs. 37k in the sixth month.
Soln:
8. 2IIM
Ascent Education’s
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Question
The captain of a cricket squad of 14 players is 28 years old. The wicket-
keeper is 32 years old. If these two players are replaced by two younger
players, the average age of the team drops by 1 year. What is the average
age of the two new players?
Que:
9. 2IIM
Ascent Education’s
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Solution
The captain of a cricket squad of 14 players is 28 years old. The wicket-
keeper is 32 years old. If these two players are replaced by two younger
players, the average age of the team drops by 1 year. What is the average
age of the two new players?
Soln:
Number * Average = Total
14 a 14a
2 - 60
12 - 14a – 60
2 X 14a – 60 + 2x
14 a – 1 14(a - 1)
11. 2IIM
Ascent Education’s
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Question
The average age of the students of class A comprising 25 students is 19
years and that of the students of class B comprising 15 students is 11
years. What is the average age of the students of the two classes taken
together?
Que:
12. 2IIM
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Solution
The average age of the students of class A comprising 25 students is 19
years and that of the students of class B comprising 15 students is 11
years. What is the average age of the students of the two classes taken
together?
Average age of 25 students = 19
Sum of the ages of 25 students = 25 * 19 = 475
Average age of 15 students = 11
Sum of the ages of 15 students = 15 * 11 = 165
Sum of the ages of 50 students put together = 475 + 165 = 640
Average age of the two classes together = 16
40
640
=
Soln:
13. 2IIM
Ascent Education’s
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Question
The average weight of a class comprising 29 students is 40 kgs. If the
weight of the teacher is also included, the average weight increases by
0.5 kgs. What is the weight of the teacher?
Que:
14. 2IIM
Ascent Education’s
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Solution
The average weight of a class comprising 29 students is 40 kgs. If the
weight of the teacher is also included, the average weight increases by
0.5 kgs. What is the weight of the teacher?
X = 55 kgs
Soln:
Number * Average = Total
29 40 1160
1 X X
30 40.5 1215
15. 2IIM
Ascent Education’s
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Question
30 friends go out for dinner. 12 of them spend Rs.32.5 each for the
dinner while the rest of them spend Rs.3 more than the average expense
of all 30. What was the total money spent??
Que:
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Solution
30 friends go out for dinner. 12 of them spend Rs.32.5 each for the
dinner while the rest of them spend Rs.3 more than the average expense
of all 30. What was the total money spent?
390 + 18(x + 3) = 30x => 390 + 18x + 54 = 30x
440 = 12x => x = 36.67
Soln:
Number * Average = Total
12 32.5 390
18 X + 3 18(x + 3)
30 X 30x
17. 2IIM
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Question
The range of the height of male members in a team is 9 cms, and that of
the female members in the team is 8 cms. What is the range of the height
of the team if the shortest man in the team is 3 cms taller than the
shortest woman in the team?
Que:
18. 2IIM
Ascent Education’s
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Solution
The range of the height of male members in a team is 9 cms, and that of
the female members in the team is 8 cms. What is the range of the height
of the team if the shortest man in the team is 3 cms taller than the
shortest woman in the team?
Soln:
9 cm
Shortest male Tallest male
8 cm
Shortest female Tallest female
19. 2IIM
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Solution
Soln:
8 cm
Shortest female Tallest female
Shortest male
3cm
Range = 3 + 9 = 12 cm
Tallest male
20. 2IIM
Ascent Education’s
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Question
The median of 68, 93, 109, x, y, and 97 is 97. What is the least possible
average of x and y?
Que:
21. 2IIM
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Solution
The median of 68, 93, 109, x, y, and 97 is 97. What is the least possible
average of x and y?
68, 93, 97, x, y, 109
Median = 97
Median = Average of 3rd
and 4th
term.
There is already one term than is 97
The only was the median can be 97 is if one of x, y is also 97.
So, assuming x =97, the numbers are 68, 93, 97, 109 and y. y has to be
greater than or equal to 97.
For the least possible average of x and y. y should be 97.
Least possible averages =
Soln:
97
2
9797
2
yx
=
+
=
+
Editor's Notes
There is not much to talk of on percentages, state the obvious and go on to 1-2 examples.
There is not much to talk of on percentages, state the obvious and go on to 1-2 examples.
This is a brilliant framework. It works for almost all questions. For the next 5-6 questions, use this framework.
