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Averages
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Averages
Averages are an important topic in the Quantitative Aptitude section of most placement tests and competitive exams. Averages, also known as arithmetic means, are used to represent the central value of a group of numbers.
Questions on averages test a candidate’s ability to:
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Perform basic calculations
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Understand numerical relationships
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Solve real-life data problems
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Apply logic with numbers
Arithmetic Mean
Definition
The arithmetic mean of a set of numbers is the sum of all values divided by the number of values.
Formula:
Arithmetic Mean = (Sum of all values) / (Number of values)
Example 1
Find the average of:
10, 15, 20, 25, 30
Average = (10 + 15 + 20 + 25 + 30) / 5
= 100 / 5
= 20
Example 2
The test scores of five students are:
85, 90, 92, 88, 95
Average = (85 + 90 + 92 + 88 + 95) / 5
= 450 / 5
= 90
Example 3
Monthly salaries (in dollars):
2500, 3000, 2800, 3200, 2700, 2900, 3100
Average = 20200 / 7
≈ 2885.71
Weighted Average
Definition
A weighted average is used when different values have different levels of importance (weights).
Formula:
Weighted Average =
(Sum of value × weight) / (Sum of weights)
Example 1
Marks:
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Quizzes: 80 (30%)
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Assignments: 90 (40%)
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Final exam: 70 (30%)
Weighted score:
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80 × 0.30 = 24
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90 × 0.40 = 36
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70 × 0.30 = 21
Total = 24 + 36 + 21 = 81
Weighted average = 81
Example 2
Fruit prices and quantities:
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Apples: $1.50 × 30 = $45
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Oranges: $2.00 × 20 = $40
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Bananas: $0.75 × 50 = $37.50
Total revenue = $122.50
Total quantity = 100 pieces
Weighted average price = 122.50 / 100
= $1.225
Average Speed
Definition
Average speed is the total distance covered divided by the total time taken.
Formula:
Average Speed = Total Distance / Total Time
Example 1
A car travels 250 km in 5 hours.
Average speed = 250 / 5
= 50 km/h
Example 2
A cyclist travels:
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60 km in 3 hours
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80 km in 4 hours
Total distance = 140 km
Total time = 7 hours
Average speed = 140 / 7
= 20 km/h
Note:
Average speed is not the same as the average of speeds. Always use total distance ÷ total time.
Average Age Problems
Example 1
Family ages:
20, 22, 24, 18, 26
Average age = (20 + 22 + 24 + 18 + 26) / 5
= 110 / 5
= 22 years
Example 2
There are 30 students in a class.
The average age must be 11 years.
Total required age = 30 × 11 = 330
Sum of 29 students’ ages = 319
Age of 30th student =
330 − 319 = 11 years
Averages Combined with Other Concepts
Average questions may also involve:
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Percentages
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Ratios
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Profit and loss
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Salary increases
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Population growth
Example
The average salary of employees increases by 10%.
If the original average salary was $40,000:
New average = 40,000 + 10% of 40,000
= 40,000 + 4,000
= $44,000
Tips for Solving Average Problems
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Use the basic average formula whenever possible.
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Convert percentages into numbers before calculating.
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In speed problems, use total distance and total time.
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For missing value problems, use:
Total sum = Average × Number of items
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Practise different types of average questions to improve speed and accuracy.
