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

### INTRODUCTION

Average is a number expressing the central or typical value in a set of data, in particular the mode, median, or (most commonly) the mean, which is calculated by dividing the sum of the values in the set by their number.

### 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?

1. 65.94
2. 53.83
3. 67.20
4. 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