Average Notes for SSC Exams

Average is an easy and scoring chapter of SSC Quantitative Aptitude. One to three questions come from it in each Tier 1 paper, and it is also used in data interpretation. These average notes for SSC explain every formula in simple words, with solved examples and practice questions.

What Is Average?

The average (or arithmetic mean) of a set of numbers is their sum divided by the number of items.

• Average = Sum of observations / Number of observations.
• Sum = Average x Number of observations.
• The average always lies between the smallest and the largest value.
• If every number is increased by k, the average also increases by k.
• If every number is multiplied by k, the average is also multiplied by k.

Important Average Formulas

Replacement and Addition of a Member

• When a new member joins, the new member's value = new average + (old group size) x (change in average).
• When a member leaves, the leaving member's value = new average - (new group size) x (change in average) in the case of a rise.
• When a person is replaced, the difference between the new and the old person = number of persons x change in average.

For example, if the average weight of 8 persons rises by 2.5 kg when a person of 65 kg is replaced, the new person weighs 65 + 8 x 2.5 = 85 kg.

Weighted Average and Average Speed

When groups have different sizes, we use the weighted average: multiply each group's average by its size, add them and divide by the total number. For speed, the average is not the simple mean of the two speeds when the distances are equal. The correct formula is 2xy / (x + y). For speeds 40 km/h and 60 km/h over the same distance, the average speed is 2 x 40 x 60 / 100 = 48 km/h.

Solved Examples

Example 1: Find the average of 12, 15, 18, 21 and 24.
Solution: Sum = 90 and number = 5. Average = 90 / 5 = 18.

Example 2: The average of 5 numbers is 20. When a sixth number is added, the average becomes 22. Find the sixth number.
Solution: New sum = 22 x 6 = 132. Old sum = 20 x 5 = 100. Sixth number = 132 - 100 = 32.

Example 3: Find the sum of the first 20 even numbers.
Solution: Sum = n (n + 1) = 20 x 21 = 420.

Example 4: The average weight of 8 persons increases by 2.5 kg when a person weighing 65 kg is replaced by a new person. Find the weight of the new person.
Solution: New person = 65 + 8 x 2.5 = 85 kg.

Example 5: A car goes from A to B at 40 km/h and returns at 60 km/h. Find the average speed.
Solution: Average speed = 2 x 40 x 60 / (40 + 60) = 4800 / 100 = 48 km/h.

Example 6: In class A, 30 students have an average mark of 60, and in class B, 20 students have an average mark of 70. Find the average of all 50 students.
Solution: Total marks = 30 x 60 + 20 x 70 = 1800 + 1400 = 3200. Average = 3200 / 50 = 64.

Quick Tips to Solve Faster

• Always work with the sum (average x number) when numbers are added, removed or replaced.
• Use the change in the average x the number of items to find the replaced value directly.
• For consecutive numbers, the average is the middle number.
• Use 2xy/(x + y) only when the distances are equal. If the times are equal, use the simple average.
• Check that the average lies between the smallest and the largest numbers.

Common Mistakes to Avoid

• Taking the simple average of two speeds when the distances are equal.
• Forgetting to change the number of items after adding or removing a member.
• Dividing by the wrong number while finding the combined average.
• Mixing the sum formulas of even and odd numbers.
• Not converting units before averaging.

Quick Revision Points

• Average = Sum / Number.
• Average of first n natural numbers = (n + 1) / 2.
• Average speed for equal distances = 2xy / (x + y).
• Combined average = (n1a1 + n2a2) / (n1 + n2).
• Change in total = change in average x number of items.

Practice Questions With Answers

1. Find the average of 7, 9, 11, 13 and 15.
   Answer: 11 (Sum = 55).
2. Find the average of the first 25 natural numbers.
   Answer: 13 ((25 + 1) / 2).
3. The average of 6 numbers is 15. If one number, 25, is removed, what is the average of the remaining numbers?
   Answer: 13 ((90 - 25) / 5).
4. The average age of 20 students is 14 years. With the teacher, the average becomes 15. Find the teacher's age.
   Answer: 35 years (15 x 21 - 14 x 20).
5. The average of three numbers is 24. If two of them are 20 and 26, find the third.
   Answer: 26 (72 - 46).
6. A person travels equal distances at 30 km/h and 20 km/h. Find the average speed.
   Answer: 24 km/h (2 x 30 x 20 / 50).
7. Find the average of the first five multiples of 6.
   Answer: 18 ((6 + 12 + 18 + 24 + 30) / 5).
8. The average of four consecutive even numbers is 15. Find the largest number.
   Answer: 18 (Numbers are 12, 14, 16, 18).
9. The sum of 5 numbers is 135. Find their average.
   Answer: 27 (135 / 5).
10. The average marks of 40 students is 52. If 10 students have an average of 40, find the average of the other 30.
    Answer: 56 ((2080 - 400) / 30).

How to Practise This Chapter

1. Learn the formulas in the table until you can write them without looking.
2. Solve the solved examples again on your own, without reading the solution.
3. Attempt the practice questions above with a timer of 10 minutes.
4. Solve the matching practice papers to test yourself in exam style.
5. Check the previous year papers to see how SSC frames this topic.

Related Notes and Practice Papers

• Percentage Notes
• Ratio and Proportion Notes
• Speed, Distance and Time Notes
• Time and Work Notes
• SSC Percentage Practice Paper

Explore More SSC Subjects

SSC exams test many subjects, so connect this topic with the related subjects below:

• Reasoning Notes
• Statistics Notes
• Indian Economy Notes
• English Notes
• General Awareness Notes
• All SSC subjects and notes

Frequently Asked Questions

What is average in simple words?

Average is the sum of all values divided by the number of values. It tells us the central value of the data.

How many questions come from average in SSC exams?

One to three questions usually come from average, and many data interpretation questions use the same concept.

What is the formula for average?

Average = Sum of observations / Number of observations.

What is the average of the first n natural numbers?

It is (n + 1) / 2.

How is average speed calculated?

For equal distances use 2xy / (x + y). In general, average speed = total distance / total time.

What is a weighted average?

A weighted average is used when the groups have different sizes. Multiply each average by its size, add them and divide by the total number.

What happens to the average when a number is replaced?

The change in the total equals the difference between the new and old numbers, and it is divided by the number of items to get the change in average.

Can the average be more than the largest number?

No, the average always lies between the smallest and the largest value.

How should I practise average questions?

Learn the formulas, solve the examples and then practise the timed questions in data interpretation and previous year papers.