Average is an important topic in Quantitative Aptitude and Numerical Ability for SSC, RRB, Banking, Defence, Police, and other competitive examinations.
In the previous chapters of Arithmetic, we covered important topics such as Percentage, Profit, Loss & Discount, Ratio & Proportion, and Simple & Compound Interest (SI & CI). Building on these concepts, this chapter focuses on the concept of Average, important formulas and shortcuts, different types of Average questions, word problems, Weighted Average, practice questions, and Previous Year Questions (PYQs) of competitive exams maths.
For complete preparation of Competitive Exams Maths and Numerical Ability, you can also explore our dedicated learning sections:
- Quantitative Maths Notes – Chapter-wise notes covering important Quantitative Aptitude topics.
- Quantitative Maths Formula Section – Important formulas arranged chapter-wise for quick revision.
- Quantitative Maths Practice Questions – Chapter-wise questions to practise the concepts we have learned.
- Previous Year Questions (PYQs) – Solved questions from SSC, RRB, Banking, Defence, Police, and other competitive examinations.
You can also explore our Competitive Exams Maths Syllabus section to understand the Maths and Numerical Ability topics asked in different examinations and use our Math Calculators to verify answers and strengthen our understanding.
If you spot an error, have a suggestion, or would like us to cover something additional, please contact us.
So, let’s start learning Average.
What is Average in Maths?
An average is a number that we get when we add two or more values and divide their sum by the number of values.
The average calculated in this way is also called the Arithmetic Mean, or simply the Mean.
Example 1
Suppose we have to find the average of 1, 2, and 3.
First, add the numbers:
1 + 2 + 3 = 6
There are 3 numbers, so:
Average = 6 ÷ 3 = 2
Therefore, the average of 1, 2, and 3 is 2.
Example 2
Apsara scored 80 marks in Maths, 70 marks in Physics, and 60 marks in Chemistry. Find her average marks.
Solution
Total Marks:
80 + 70 + 60 = 210
Number of Subjects = 3
Therefore:
Average = 210 ÷ 3 = 70
So, Apsara’s average marks are 70.
In Simple Words
To find an average, we follow two basic steps:
Step 1: Add all the values.
Step 2: Divide the total by the number of values.
Basic Average Formula
Average = Sum of all values ÷ Number of values
Example 3:
What will be the average value of these numbers: 465, 345, 650, 265 & 310?
Solution
So, by using the formula of average:
Average = Sum of all values ÷ Number of values
Sum of all values:
465 + 345 + 650 + 265 + 310 = 2035
Number of values: 5
Average value:
2035 ÷ 5 = 407
Therefore, the average value of 465, 345, 650, 265 & 310 is 407.
This is the application of the basic Average formula. However, competitive-exam questions often use different variations and shortcuts.
We have explained these formulas and shortcuts with examples on our Average Formula with Examples and Explanations page.
Types of Average Questions: Average Questions with Answers and Solutions
Competitive exams ask Average questions in several forms, including:
- Average Age
- Average Marks
- Average Population
- Weighted Average
- Combined or Addition of Averages
- Missing Values in an Average
- Average Income or Salary
- Average-based questions involving different real-life contexts
Example 4:
The weight of six RRB Group D candidates is recorded as 52 kg, 61 kg, 68 kg, 57 kg, 74 kg and 63 kg. What is the average weight of all six candidates?
Solution
Step 1: Find the sum of all weights
52 + 61 + 68 + 57 + 74 + 63 = 375 kg
Step 2: Count the number of candidates
Number of candidates = 6
Step 3: Apply the average formula
Average = Sum of all values ÷ Number of values
= 375 ÷ 6
= 62.5 kg
Therefore, the average weight of the six RRB Group D candidates is 62.5 kg.
We cover these variations with questions, answers, and detailed solutions in our Average Questions with Answers and Solutions section.
Quick Average Shortcuts for Competitive Exams
Here are some useful shortcuts for solving Average questions quickly.
Our Average Formula, Average Questions with Answers and Solutions, and Average PYQs sections also explain question-specific shortcuts wherever they help save calculation time.
Total = Average × Number of Observations
This is the key relationship used to quickly find the total, average, or number of observations when the other two values are known.
Example 5:
The average age of two SSC aspirants is 36 years. The ratio of their ages is 7 : 5 respectively. What is the age of the younger SSC aspirant?
Solution
Step 1: Find the total age
Average age = 36 years
Number of persons = 2
Total age = Average × Number of persons
= 36 × 2
= 72 years
Step 2: Use the age ratio
Ratio of their ages = 7 : 5
Total parts = 7 + 5 = 12 parts
Value of 1 part = 72 ÷ 12 = 6 years
Step 3: Find the younger SSC aspirant’s age
Younger age = 5 × 6
= 30 years
Therefore, the age of the younger SSC aspirant is 30 years.
To learn how ratios are used to divide a total into proportional parts, see our Ratio and Proportion section.
Average Practice Questions
Practice Question 1
Apsara scored 80 marks in Maths, 85 marks in Physics and 75 marks in Chemistry in her Class 10 examination. Her classmate scored 70, 95 and 75 marks in the same subjects, respectively. Apsara’s average marks are higher than her classmate’s average marks. Is this statement True or False?
Practice Question 2
A Lucknow-bound train has an average of 60 passengers in three coaches—S5, S6 and S7. Coach S5 has 65 passengers and Coach S6 has 55 passengers. How many passengers are there in Coach S7?
Answer Key
- False
- 60 passengers
Once you have learned the Average concepts and formulas and solved questions covering different variations, test your understanding with our Average Practice Questions with Answers.
This practice section includes MCQs, True/False questions, Fill in the Blanks, and word problems to help you improve your calculation skills, speed, and accuracy for competitive examinations.
Average PYQs for Competitive Exams
Average questions are often asked in various competitive exams such as SSC, RRB, Defence, Banking and Police exams. Practicing these questions is important to improve your calculation skills, speed and accuracy, which can help you score better in competitive examinations.
Below is an example based on a previous-year SSC question. We have changed the numbers and context to make the question more relatable while retaining the same mathematical concept.
Example 6:
An SSC Maths coaching centre purchased 15 study chairs and 5 study tables for ₹10,500. If the average cost of a table is ₹1,350, what is the average cost of a chair?
Solution
Step 1: Find the total cost of the tables
Average cost of one table = ₹1,350
Number of tables = 5
Total cost of tables = Average cost × Number of tables
= ₹1,350 × 5
= ₹6,750
Step 2: Find the total cost of the chairs
Total cost of chairs and tables = ₹10,500
Total cost of chairs:
= ₹10,500 − ₹6,750
= ₹3,750
Step 3: Find the average cost of one chair
Number of chairs = 15
Average cost of one chair = Total cost of chairs ÷ Number of chairs
= ₹3,750 ÷ 15
= ₹250
Therefore, the average cost of one chair is ₹250.
Our Average PYQs for SSC, RRB, Banking & Defence Exams section lists multiple PYQs with detailed solutions for practice.
Related Quantitative Aptitude Topics
Percentage → Averages often involve percentage changes.
Ratio & Proportion → Useful for combined and weighted averages.
Profit, Loss & Discount → Average cost and profit applications.
Simple & Compound Interest → Important quantitative arithmetic foundation.
Age Problems → Useful for questions involving the average age of individuals, families and groups.
Mixture & Alligation → Strongly related to weighted averages.
Time, Speed & Distance → Useful for Average Speed questions.
FAQ on Average
What is the formula for Average?
Average = Sum of all values ÷ Number of values
What happens to Average when a new value is added?
When a new value is added, the total average may increase, decrease, or remain the same, depending on the value of the new number.
Is Average Speed the same as ordinary Average?
No, Average Speed is calculated using total distance travelled ÷ total time taken, which is different from the ordinary Average questions we solve in Maths.
Which competitive exams ask average questions?
Average is included in the syllabus of most competitive exams with a Quantitative Aptitude section, such as SSC, RRB, Banking, Defence, Police, and other State and Central Government exams. So, preparing average is important for these examinations.