Average Aptitude Concepts and Formulas
Points to remember:
1) The average of n quantities of the same kind is equal to the sum of all the quantities divided by the number of quantities;
Average = ![Apti Average 1](https://static.javatpoint.com/aptitude/images/average1.png)
Sum of quantities = Average ∗ Number of quantities
Number of quantities = ![Apti Average 2](https://static.javatpoint.com/aptitude/images/average2.png)
2) Average of two or more than two groups;
If the number of quantities in two groups are n1 and n2 respectively and their individual average is X and Y respectively, the combined average of the two groups is given by;
= ![Apti Average 3](https://static.javatpoint.com/aptitude/images/average3.png)
3) If the average of n1 quantities is X and the average of n2 quantities out of n1 quantities is Y, the average of the remaining quantities is given by;
= ![Apti Average 4](https://static.javatpoint.com/aptitude/images/average4.png)
4) The average of n quantities is equal to X. One quantity of value P is replaced with a new quantity having value Q the average of quantities becomes Y. Then Q is given by;
Q = P+n (Y-X)
5) The average of n quantities is equal to X. If we remove one quantity the average becomes Y, the value of the removed quantity is given by;
= n(X - Y) + Y
And, if the average of n quantities is equal to X and on adding a new quantity the average becomes Y, the value of new quantity is given by;
= n ( Y - X) + Y
6) Average of numbers:
1) Natural numbers:
- The average of first n consecutive natural numbers is given by; =
![Apti Average 5](https://static.javatpoint.com/aptitude/images/average5.png)
- The average of square of first n consecutive natural numbers is given by; =
![Apti Average 6](https://static.javatpoint.com/aptitude/images/average6.png)
- The average of cubes of first n consecutive natural numbers is given by; =
![Apti Average 7](https://static.javatpoint.com/aptitude/images/average7.png)
2) Even numbers:
- The average of first n consecutive even numbers is given by;
= n + 1
- Also, the average of first n consecutive even numbers starting from 2 to X, where the last even number is X, is given by;
= ![Apti Average 8](https://static.javatpoint.com/aptitude/images/average8.png)
- The average of square of first n consecutive even numbers is given by;
= ![Apti Average 9](https://static.javatpoint.com/aptitude/images/average9.png)
- Also, the average of square of first n consecutive even numbers starting from 2 to X, where the last even number is X, is given by;
= ![Apti Average 10](https://static.javatpoint.com/aptitude/images/average10.png)
3) Odd numbers:
- The average of first n consecutive odd numbers is equal to n.
- Also, the average of first n consecutive odd numbers starting from 1 to X, where the last odd number is X is given by;
= ![Apti Average 11](https://static.javatpoint.com/aptitude/images/average11.png)
- The average of square of first n consecutive odd numbers starting from 1 to X, where the last odd number is X, is given by;
= ![Apti Average 12](https://static.javatpoint.com/aptitude/images/average12.png)
Some quicker methods:
- The average of n numbers is X. If each number is multiplied by Y, the new average is given by;
= Initial average ∗ Y
- The average age of a group of boys is given. If the new average age after a boy joins the group is also given, the age of new boy is given by;
Age of new boy = New average + number of boys initially ∗ increase in average
- The average weight of a group of persons is given. If we replace a person in the group with another person and the new average is increased,
The weight of new person = weight of the removed person + no. of persons ∗ increase in average.
- The average of the marks obtained by students is given. The average of marks obtained by the passed students and failed students are also given, then
Number of passed candidates = ![Apti Average 13](https://static.javatpoint.com/aptitude/images/average13.png)
And, Number of failed students =![Apti Average 14](https://static.javatpoint.com/aptitude/images/average14.png)
Average Aptitude Test Paper 1
Average Aptitude Test Paper 2
Average Aptitude Test Paper 3
Average Aptitude Test Paper 4
Average Aptitude Test Paper 5
Average Aptitude Test Paper 6
Average Aptitude Test Paper 7
Average Aptitude Test Paper 8
|