In this section, the following topics are discussed with examples

**Introduction****General method of finding averages****Average determination based on number of elements****Odd Number Series****Even Number Series**

**Average of first ‘n’ numbers****Average of square first ‘n’ numbers**

### General method of finding averages:

An average or arithmetic mean of given n number of items is a total sum divided by total number of items given.

Therefore,

**Average= Sum of Total Items Given/Number of Items**

Let’s say If we have Given n Items: n1, n2, n3, ….n

Then, **Total Average = (n1 + n2 + n3 + ——– + n) / n**

## The healthiest competition occurs when average people win by putting above average effort.

COLIN POWELL

#### Example 1

Ram scored 89,46,74,69,58 in all the five subjects in a class test. Find the average mark scored by Ram?

- 65.94
- 53.83
- 67.20
- 63.71

**Solution:**

Step 1: To calculate average add all the terms given in as the marks

89 + 46 + 74 + 69 + 58 = 336

Step 2: Now divide the above answer with the number of elements present (i.e.,) n=5

And thus the resultant of that will be your average.

Avg= 336/5= 67.20.

#### Average determination based on number of elements:

Based on the number of elements, if and only if the elements are in Arithmetic progressions,(i.e., there should be the same common difference between every term of the given series.)

**ODD Numbered Series****:** (n = some odd number)

Let’s look at some examples below

Example 2

1. 3,5,7,9,11,13,15,17,19 (n = 9)

2. 2,3,4,5,6,7,8(n=7)

3. 0.25,0.50,0.75,1.0,1.25(n=5)

**EVEN Numbered Series:**** **(n = some even number)

Let’s look at some examples below

**Example 4:**

1. 3,5,7,9,11,13,15,17 (n = 8)

2. 2,3,4,5,6,7 (n = 6)

3. 0.25,0.50,0.75,1.0 (n = 4)

In even numbered series, the middle of the middle two elements is the answer for that series, this above series is also called as asymmetric series.

#### Average of First ‘n’ Numbers :

To find the average of first n numbers if they are in A.P. ,(say natural numbers or whole numbers or even numbers or odd numbers etc…) then we can use this formula

Average = (n + 1)/2

#### Average of Square First ‘n’ numbers :

To find the square of first n numbers , we can use

Average = (n+1)(2n+1) / 6

#### Example

The average of ages of 10 persons in a class was 32. When new person joins the class the average weight increases by 4. Find the weight of the new person added ?

a) 61

b) 80

c) 75

d) 76

**Sol:**

Total age of 10 persons = 10 × 32 = 320

Total age of 11 persons = 11 × 36 = 396 (as the new average is 4 more than present average)

So the age of the person joining is = 396 – 320 = 76