We have covered the basics of Average. In this section, we will focus on Average formulas with simple explanations and examples. The formulas are applied to different types of questions to help aspirants understand how and when to use them in competitive examinations.
Quick Note: Average Formula
| Formula Name | Formula |
| Total | Total = Average × Number of times present |
| Average | Average = Total ÷ Number of times present |
| Number of times present | Number of times present = Total ÷ Average |
| Weighted Average | Weighted Average = [(Number in Group 1 × Average of Group 1) + (Number in Group 2 × Average of Group 2)] ÷ (Number in Group 1 + Number in Group 2) |
Here, “number of times present” means the number of observations or values being considered.
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Average Formula Derivation
Suppose an SSC coaching institute wants to give a special discount to a student. The condition is that the student’s average marks in Physics, Chemistry and Mathematics must be more than 60 out of 100.
The student scores:
- Physics = 65
- Chemistry = 58
- Mathematics = 67
Now the institute needs to check whether the student qualifies.
First, find the total marks:
65 + 58 + 67 = 190
There are 3 subjects, so the average marks are:
Average = Total Marks ÷ Number of Subjects
= 190 ÷ 3 = 63.33
Since 63.33 > 60, the student qualifies for the discount.
But What Does Average Actually Mean?
Think of the same 190 marks being distributed equally among the 3 subjects.
Instead of:
65, 58, 67
we could imagine giving each subject an equal share:
63.33, 63.33, 63.33
The total remains the same:
63.33 × 3 = 190
This gives us the fundamental relationship:
1. Total = Average × Number of times present
2. Average = Total ÷ Number of times present
3. Number of times present = Total ÷ Average
Example 1: Find the Average
What will be the average of these numbers?
191, 199, 291, 319 and 430
There are 5 numbers.
First, find their total:
191 + 199 + 291 + 319 + 430 = 1430
Now use the formula:
Average = Total ÷ Number of numbers
Average = 1430 ÷ 5 = 286
Answer: 286
Example 2: Find the Total
The average of 5 numbers is 286. What is their total?
We know:
Total = Average × Number of numbers
So:
Total = 286 × 5
Total = 1430
Answer: 1430
Example 3: Find the Number of Numbers
The total of some numbers is 1430 and their average is 286. How many numbers are there?
We know:
Number of numbers = Total ÷ Average
So:
Number of numbers = 1430 ÷ 286
Number of numbers = 5
Answer: 5 numbers
Example 4: Average When a Number Is Added
The average of 5 numbers—191, 199, 291, 319 and 430—is 286. What will be the new average if one more number, 580, is added to the series?
First, find the original total using:
Total = Average × Number of numbers
Original Total = 286 × 5 = 1430
Now add the new number:
New Total = 1430 + 580 = 2010
After adding 580, there are 6 numbers.
Therefore:
New Average = 2010 ÷ 6 = 335
Answer: 335
Example 5: Average When a Number Is Removed
The average of 5 numbers—191, 199, 291, 319 and 430—is 286. What will be the new average if the number 430 is removed from the series?
First, find the original total:
Original Total = Average × Number of numbers
= 286 × 5 = 1430
Now remove 430:
New Total = 1430 − 430 = 1000
After removing 430, there are 4 numbers left.
Therefore:
New Average = 1000 ÷ 4 = 250
Answer: 250
Example 6: Average When a Number Is Replaced
The average of 5 numbers—191, 199, 291, 319 and 430—is 286. What will be the new average if 430 is replaced by 580?
First, find the original total:
Original Total = Average × Number of numbers
= 286 × 5 = 1430
Now replace 430 with 580:
New Total = 1430 − 430 + 580
= 1580
The number of numbers remains 5.
Therefore:
New Average = 1580 ÷ 5 = 316
Answer: 316
Example 7: Finding the Missing Number Using Average
The average of 5 numbers—191, 199, 291, 319 and one missing number—is 286. Find the missing number.
First, find the total of all 5 numbers:
Total = Average × Number of numbers
= 286 × 5 = 1430
Now find the total of the four known numbers:
191 + 199 + 291 + 319 = 1000
Therefore:
Missing Number = 1430 − 1000
= 430
Answer: 430
Example 8: Change in Average
The average of 5 numbers is 286. If each number is increased by 20, what will be the new average?
First, find the original total:
Original Total = Average × Number of numbers
= 286 × 5 = 1430
Since each of the 5 numbers is increased by 20, the total increases by:
20 × 5 = 100
So, the new total is:
1430 + 100 = 1530
The number of numbers remains 5.
Therefore:
New Average = 1530 ÷ 5
= 306
Answer: 306
Example 9: Combined Average — A Weighted Average Application
The average marks of 5 RRB ALP aspirants in a mock test is 286, while the average marks of another 3 RRB ALP aspirants is 250. What is the average marks of all 8 RRB ALP aspirants together?
First, find the total marks of the first 5 aspirants:
Total = 286 × 5 = 1430
Now find the total marks of the other 3 aspirants:
Total = 250 × 3 = 750
Therefore, the total marks of all 8 aspirants are:
1430 + 750 = 2180
Total number of aspirants:
5 + 3 = 8
Therefore:
Combined Average = 2180 ÷ 8
= 272.5
Answer: 272.5
Weighted Average Formula
The Combined Average question in Example 9 is also an application of the Weighted Average Formula.
In that example, the two groups have different numbers of aspirants:
- Group 1: 5 aspirants, average marks = 286
- Group 2: 3 aspirants, average marks = 250
Since the groups contain different numbers of aspirants, their averages do not have equal contribution to the combined average.
For two groups, the formula is:
Weighted Average = [(Number in Group 1 × Average of Group 1) + (Number in Group 2 × Average of Group 2)] ÷ (Number in Group 1 + Number in Group 2)
Applying the Formula to Example 9
Weighted Average = [(5 × 286) + (3 × 250)] ÷ (5 + 3)
= (1430 + 750) ÷ 8
= 2180 ÷ 8
= 272.5
Answer: 272.5
Practice Questions
Practice Question 1
The average age of 6 RRB NTPC aspirants is 24 years. If the age of one more aspirant is 31 years, what will be the new average age of all 7 aspirants?
Answer: 25 years
Practice Question 2 —
In an SSC mock test, 8 students have an average score of 72 marks, while 12 other students have an average score of 84 marks. What is the average score of all 20 students together?
Answer: 79.2 marks
Ready for more? Solve our Average Practice Questions to practice different Average concepts and improve your speed and accuracy for competitive exams.
What We Learned in Average Formula
Total = Average × Number of observations
Average = Total ÷ Number of observations
Number of observations = Total ÷ Average
How to find the new average when a number is added, removed, or replaced
How to find a missing number using the average
How a change in each number affects the average
How to calculate a combined/weighted average for different groups
Related Topics
Frequently Asked Questions — Average Formula
1. What is the formula for finding the total?
Total = Average × Number of times present (Number of observations)
2. What is the formula for finding the average?
Average = Total ÷ Number of times present (Number of observations)
3. How do I find the number of times present (number of observations)?
Number of observations = Total ÷ Average
4. What is the weighted average formula?
Weighted Average = [(Number in Group 1 × Average of Group 1) + (Number in Group 2 × Average of Group 2)] ÷ (Number in Group 1 + Number in Group 2)
5. What does “number of times present” mean?
It means the number of observations or values being considered. For example, if an average is calculated for 5 numbers, the number of times present is 5.