# Rapid Revision for CSIR NET Part A: Formula Sheets on Average - Check Here!!!

By Astha Singh|Updated : February 10th, 2022

CSIR NET Part-A Formula Sheet: During the preparation, the candidates study different formulas to solve problems, but at the last moment, these formulas might not be remembered by the candidates due to exam fear or pressure. We at BYJU'S Exam Prep do not want our students to lag anywhere during the preparation, so we have come up with a concept of a Formula Sheet that will help them revise the important formulas at the last moment. This formula sheet will be a short revision tool and contain only important formulas that need to be studied at the last minute to boost the score. Our experienced subject-matter experts have meticulously designed this CSIR NET General Aptitude Formula Sheet to provide you with the best authentic material.

In this article, we will cover the CSIR NET General Aptitude Most Important Formulas of Average. Aspiring candidates can check all the most important formulas of Average for the last minute revision. Scroll down the full article to find out!

## Formula Sheet On Average

Definition:
It is defined as the sum of all the terms (or data) divided by a total number of terms. Basic Formulas:
1.Average of first n natural numbers = (n+1) / 2
2. Sum of first n natural numbers =
3.Average of squares of first n natural numbers = (n+1) (2n+1) / 6
4.Average of cubes of first n natural numbers = n (n+1)2 / 4
5.Average of first n even numbers = n + 1
6.Sum of first n even numbers = n(n +1)
7.Average of squares of first n even numbers = 2 (n+1) (2n+1) / 3
8. Average of the cube of first n even numbers = 2n (n+1)2
9. Average of first n odd numbers = n
10. Sum of first n odd numbers = n2
11.Average of squares of first n odd numbers = (2n+1) (2n-1) / 3
12. Average of cube of first n odd numbers = n(2n2 – 1)
13.Average of n consecutive numbers = (First number + Last number)/2
14. The average of n consecutive numbers is always the middle term of all the numbers when n is an odd number. And when n is an even number, the average of all consecutive numbers is always the mean of two middle terms.

Some special points:
1. The average of given observations always lies between the value of the highest term and the value of the lowest term.
2. If the value of each number is divided by the same value “a”, then the average of all given numbers will also get divided by “a”.
3. If the value of each number is multiplied by the same value “a”, then the average of all numbers will also get multiplied by “a”.
4. If the value of each number is decreased by the same value “a”, then the average of all numbers will also get decrease by “a”.
5. If the value of each number is increased by the same value “a”, then the average of all numbers will also get increase by “a”.

Some Direct Formulas:
1. If the average of “x” numbers is “p” and that of “y” numbers is “q”, then the average of (x + y) numbers
2. If the average of “x” numbers is “p” and that of “y” numbers taken out of “x” numbers is “q”, then the average of the rest of the numbers
3. If the average of “n” quantities is equal to “p” when a particular quantity is removed, the average becomes “q”. Then the value of quantity removed is = [n (p - q) + q]

Examples:
1. The sum of 17 consecutive numbers is 289. The sum of another 10 consecutive numbers, whose first term is 5 more than the average of the first set of consecutive numbers, is:
A. 300
B. 285
C. 265
D. 315

Solution- 2. A player has a certain average for 15 innings. In the 16th inning, he scores 120, thereby, his average increases by 6 runs. What is the new average?
A. 8
B. 30
C. 24
D. 20

Solution-
Let the average of 15 innings be x
According to the question,
⇒ (15x + 120)/16 = x + 6
⇒15x + 120 = 16x + 96
x = 24
Hence, new average = 24 + 6 = 30.

3. The average age of fifteen persons is 32 years. If two more persons are added, then the average is increased by 3 years. The new persons have an age difference of 7 years between them. The age (in years) of the elder among the new persons is:

A. 58
B. 61
C. 50
D. 54

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