Average is an important topic in mathematics and quantitative aptitude. It is useful for school exams, government job exams, banking exams, SSC, railway exams, entrance tests and placement tests. Many questions from this topic look short, but they need a clear understanding of formula, method and calculation steps.
This lesson explains average in simple language. It includes meaning, important terms, formulas, shortcut ideas, solved examples, common mistakes, practice questions and frequently asked questions. The aim is to make the topic easy to learn for beginners and useful for exam preparation.
Before solving any question, read the statement carefully and write the given values separately. Then decide which formula or method is required. This small habit prevents most calculation mistakes.
What Is Average?
Average is a single value that represents a group of values. It is found by dividing the sum of all observations by the number of observations.
In aptitude exams, average questions usually test basic understanding, speed of calculation and the ability to choose the correct method quickly. A good answer should be accurate, but it should also be solved in less time.
Important Terms
| Point | Details |
|---|---|
| Observation | Each value in the given data |
| Sum | Total of all values |
| Number of observations | How many values are given |
| Average | Sum divided by number of observations |
| Weighted average | Average when values have different importance or quantities |
Key Formulas
| Point | Details |
|---|---|
| Average | Sum of observations / Number of observations |
| Sum | Average x Number of observations |
| Number of observations | Sum / Average |
| New average | New total / New number |
| Weighted average | Total weighted value / Total weight |
How to Solve Average Questions
The best method is to move step by step. First identify the given data. Second, decide what is asked. Third, choose the formula. Fourth, substitute values carefully. Fifth, check whether the answer has the correct unit or form.
For multiple-choice aptitude questions, also look at the options after doing the basic setup. Sometimes the options help you avoid long calculations. Still, never guess before understanding the question because many options are designed around common mistakes.
- Write all given observations or groups.
- Find total sum or total weighted value.
- Find the number of observations or total weight.
- Divide total by count or weight.
- Check whether the average lies within a reasonable range.
Shortcut Ideas
- If all numbers increase by x, average also increases by x.
- If all numbers decrease by x, average also decreases by x.
- If all numbers are multiplied by x, average is also multiplied by x.
- For consecutive numbers, average is the middle value.
- For equally spaced numbers, average is first plus last divided by 2.
Common Question Types
| Point | Details |
|---|---|
| Direct average | Find sum and divide by count |
| Missing number | Use sum = average x count |
| New member added | Update total and count |
| Weighted average | Use quantity or weight |
| Combined average | Add group totals and divide by total count |
Solved Examples
Example 1
Find the average of 10, 20, 30, 40 and 50.
Sum = 150 and number of values = 5. Average = 150/5 = 30.
Example 2
Average of 6 numbers is 18. Find their sum.
Sum = average x number = 18 x 6 = 108.
Example 3
Average age of 5 students is 12 years. A new student of age 17 joins. Find new average.
Old total = 5 x 12 = 60. New total = 77. New average = 77/6 = 12.83 years.
Example 4
Average of first 10 natural numbers.
The numbers are 1 to 10. Average = (1 + 10)/2 = 5.5.
Example 5
A batsman scores 40, 55, 60 and 45. Find average score.
Total = 200. Average = 200/4 = 50.
Exam Style Examples with Explanation
Exam Example 1
Average of 8 numbers is 24. If one number 32 is removed, find new average.
Total = 8 x 24 = 192. New total = 192 – 32 = 160. New average = 160/7 = 22.86.
Use total first, then adjust the removed value.
Exam Example 2
Average weight of 10 boys is 45 kg and average weight of 15 girls is 40 kg. Find combined average.
Total weight = 10 x 45 + 15 x 40 = 1050. Total students = 25. Combined average = 1050/25 = 42 kg.
For combined average, add total values, not averages directly.
Exam Example 3
The average of five consecutive odd numbers is 27. Find the largest number.
Middle number is 27. The numbers are 23, 25, 27, 29, 31. Largest = 31.
For consecutive odd numbers, average is the middle number.
Common Mistakes
- Dividing by wrong count.
- Taking average of averages without considering group sizes.
- Forgetting to update total when a number is added or removed.
- Not checking whether answer is reasonable.
- Confusing median with average.
Practice Questions
- Find average of 12, 18, 20, 30.
- Average of 7 numbers is 15. Find sum.
- Average of 10 numbers is 25. One number 40 is added. Find new average.
- Average of first 20 natural numbers.
- Average of 6 consecutive even numbers is 21. Find the numbers.
- Average marks of 30 students is 60. Total marks?
- Average of 5 values is 16. If four values are 10, 12, 18, 20, find fifth.
- Average of 20 and 40.
- Average speed for 100 km in 2 hours.
- Combined average of 5 values average 10 and 10 values average 20.
Answers to Practice Questions
- 20
- 105
- 26.36
- 10.5
- 16, 18, 20, 22, 24, 26
- 1800
- 20
- 30
- 50 km/h
- 16.67
Frequently Asked Questions
What is average?
Average is the sum of values divided by the number of values.
What is the formula of average?
Average = Sum / Number of observations.
Can average be decimal?
Yes, average can be a decimal or fraction.
What is weighted average?
Weighted average considers quantity or importance of each value.
How is average used in exams?
It is used in marks, age, speed, salary and data questions.
Revision Notes
Average represents a group by one value. Always find total first when values are added, removed, or combined.
For fast revision, remember the formula, one easy example and one common mistake. If you can explain the topic to another student in simple words, your concept is strong enough for most exam questions.
More Practice for Accuracy
Practice is very important in average. Start with direct formula questions, then solve word problems, and finally try mixed questions. While practising, write down every mistake in a small notebook. After a few days, revise only those mistakes. This improves speed and accuracy together.
In government exam questions, the language may be slightly different, but the concept remains the same. Look for keywords such as total, difference, ratio, remaining, at least, greatest, smallest, average, possible ways, or probability. These words tell you which formula should be used.
Do not try to memorise every solved question. Instead, understand the pattern behind it. Once the pattern is clear, you can solve many similar questions even when the numbers are changed.
Conclusion
Average is simple when you remember that total value is the base of every question.
Learn the basic rule first, practise solved examples, and then attempt practice questions without looking at the answers. This is the best way to become confident in average.
Additional Exam Note 12
Average questions become easier when you slow down for the first few seconds and understand the condition. Many wrong answers happen because students directly apply a remembered formula without checking whether the question asks for value, ratio, number of ways, time, quantity, or final answer.
While solving, keep units consistent and simplify numbers whenever possible. If the question contains fractions, convert them carefully. If it contains percentages, write them as fractions when that makes the calculation faster. If it contains a ratio, use variables such as x, 2x, 3x or 5x to keep the relation clear.
A useful practice method is to solve the same example in two ways: one by formula and one by logical reasoning. This builds confidence and helps in exams where time is limited. After solving, check whether the answer is reasonable. For example, an average should lie between the smallest and largest value, and a probability should never be greater than 1.
Additional Exam Note 13
Average questions become easier when you slow down for the first few seconds and understand the condition. Many wrong answers happen because students directly apply a remembered formula without checking whether the question asks for value, ratio, number of ways, time, quantity, or final answer.
While solving, keep units consistent and simplify numbers whenever possible. If the question contains fractions, convert them carefully. If it contains percentages, write them as fractions when that makes the calculation faster. If it contains a ratio, use variables such as x, 2x, 3x or 5x to keep the relation clear.
A useful practice method is to solve the same example in two ways: one by formula and one by logical reasoning. This builds confidence and helps in exams where time is limited. After solving, check whether the answer is reasonable. For example, an average should lie between the smallest and largest value, and a probability should never be greater than 1.
Additional Exam Note 15
Average questions become easier when you slow down for the first few seconds and understand the condition. Many wrong answers happen because students directly apply a remembered formula without checking whether the question asks for value, ratio, number of ways, time, quantity, or final answer.
While solving, keep units consistent and simplify numbers whenever possible. If the question contains fractions, convert them carefully. If it contains percentages, write them as fractions when that makes the calculation faster. If it contains a ratio, use variables such as x, 2x, 3x or 5x to keep the relation clear.
A useful practice method is to solve the same example in two ways: one by formula and one by logical reasoning. This builds confidence and helps in exams where time is limited. After solving, check whether the answer is reasonable. For example, an average should lie between the smallest and largest value, and a probability should never be greater than 1.
Additional Exam Note 16
Average questions become easier when you slow down for the first few seconds and understand the condition. Many wrong answers happen because students directly apply a remembered formula without checking whether the question asks for value, ratio, number of ways, time, quantity, or final answer.
While solving, keep units consistent and simplify numbers whenever possible. If the question contains fractions, convert them carefully. If it contains percentages, write them as fractions when that makes the calculation faster. If it contains a ratio, use variables such as x, 2x, 3x or 5x to keep the relation clear.
A useful practice method is to solve the same example in two ways: one by formula and one by logical reasoning. This builds confidence and helps in exams where time is limited. After solving, check whether the answer is reasonable. For example, an average should lie between the smallest and largest value, and a probability should never be greater than 1.
Additional Exam Note 18
Average questions become easier when you slow down for the first few seconds and understand the condition. Many wrong answers happen because students directly apply a remembered formula without checking whether the question asks for value, ratio, number of ways, time, quantity, or final answer.
While solving, keep units consistent and simplify numbers whenever possible. If the question contains fractions, convert them carefully. If it contains percentages, write them as fractions when that makes the calculation faster. If it contains a ratio, use variables such as x, 2x, 3x or 5x to keep the relation clear.
A useful practice method is to solve the same example in two ways: one by formula and one by logical reasoning. This builds confidence and helps in exams where time is limited. After solving, check whether the answer is reasonable. For example, an average should lie between the smallest and largest value, and a probability should never be greater than 1.
Additional Exam Note 20
Average questions become easier when you slow down for the first few seconds and understand the condition. Many wrong answers happen because students directly apply a remembered formula without checking whether the question asks for value, ratio, number of ways, time, quantity, or final answer.
While solving, keep units consistent and simplify numbers whenever possible. If the question contains fractions, convert them carefully. If it contains percentages, write them as fractions when that makes the calculation faster. If it contains a ratio, use variables such as x, 2x, 3x or 5x to keep the relation clear.
A useful practice method is to solve the same example in two ways: one by formula and one by logical reasoning. This builds confidence and helps in exams where time is limited. After solving, check whether the answer is reasonable. For example, an average should lie between the smallest and largest value, and a probability should never be greater than 1.
Additional Exam Note 21
Average questions become easier when you slow down for the first few seconds and understand the condition. Many wrong answers happen because students directly apply a remembered formula without checking whether the question asks for value, ratio, number of ways, time, quantity, or final answer.
While solving, keep units consistent and simplify numbers whenever possible. If the question contains fractions, convert them carefully. If it contains percentages, write them as fractions when that makes the calculation faster. If it contains a ratio, use variables such as x, 2x, 3x or 5x to keep the relation clear.
A useful practice method is to solve the same example in two ways: one by formula and one by logical reasoning. This builds confidence and helps in exams where time is limited. After solving, check whether the answer is reasonable. For example, an average should lie between the smallest and largest value, and a probability should never be greater than 1.
Additional Exam Note 23
Average questions become easier when you slow down for the first few seconds and understand the condition. Many wrong answers happen because students directly apply a remembered formula without checking whether the question asks for value, ratio, number of ways, time, quantity, or final answer.
While solving, keep units consistent and simplify numbers whenever possible. If the question contains fractions, convert them carefully. If it contains percentages, write them as fractions when that makes the calculation faster. If it contains a ratio, use variables such as x, 2x, 3x or 5x to keep the relation clear.
A useful practice method is to solve the same example in two ways: one by formula and one by logical reasoning. This builds confidence and helps in exams where time is limited. After solving, check whether the answer is reasonable. For example, an average should lie between the smallest and largest value, and a probability should never be greater than 1.
Additional Exam Note 24
Average questions become easier when you slow down for the first few seconds and understand the condition. Many wrong answers happen because students directly apply a remembered formula without checking whether the question asks for value, ratio, number of ways, time, quantity, or final answer.
While solving, keep units consistent and simplify numbers whenever possible. If the question contains fractions, convert them carefully. If it contains percentages, write them as fractions when that makes the calculation faster. If it contains a ratio, use variables such as x, 2x, 3x or 5x to keep the relation clear.
A useful practice method is to solve the same example in two ways: one by formula and one by logical reasoning. This builds confidence and helps in exams where time is limited. After solving, check whether the answer is reasonable. For example, an average should lie between the smallest and largest value, and a probability should never be greater than 1.
Additional Exam Note 26
Average questions become easier when you slow down for the first few seconds and understand the condition. Many wrong answers happen because students directly apply a remembered formula without checking whether the question asks for value, ratio, number of ways, time, quantity, or final answer.
While solving, keep units consistent and simplify numbers whenever possible. If the question contains fractions, convert them carefully. If it contains percentages, write them as fractions when that makes the calculation faster. If it contains a ratio, use variables such as x, 2x, 3x or 5x to keep the relation clear.
A useful practice method is to solve the same example in two ways: one by formula and one by logical reasoning. This builds confidence and helps in exams where time is limited. After solving, check whether the answer is reasonable. For example, an average should lie between the smallest and largest value, and a probability should never be greater than 1.
Additional Exam Note 28
Average questions become easier when you slow down for the first few seconds and understand the condition. Many wrong answers happen because students directly apply a remembered formula without checking whether the question asks for value, ratio, number of ways, time, quantity, or final answer.
While solving, keep units consistent and simplify numbers whenever possible. If the question contains fractions, convert them carefully. If it contains percentages, write them as fractions when that makes the calculation faster. If it contains a ratio, use variables such as x, 2x, 3x or 5x to keep the relation clear.
A useful practice method is to solve the same example in two ways: one by formula and one by logical reasoning. This builds confidence and helps in exams where time is limited. After solving, check whether the answer is reasonable. For example, an average should lie between the smallest and largest value, and a probability should never be greater than 1.
Additional Exam Note 29
Average questions become easier when you slow down for the first few seconds and understand the condition. Many wrong answers happen because students directly apply a remembered formula without checking whether the question asks for value, ratio, number of ways, time, quantity, or final answer.
While solving, keep units consistent and simplify numbers whenever possible. If the question contains fractions, convert them carefully. If it contains percentages, write them as fractions when that makes the calculation faster. If it contains a ratio, use variables such as x, 2x, 3x or 5x to keep the relation clear.
A useful practice method is to solve the same example in two ways: one by formula and one by logical reasoning. This builds confidence and helps in exams where time is limited. After solving, check whether the answer is reasonable. For example, an average should lie between the smallest and largest value, and a probability should never be greater than 1.