## Arithmetic Mean

Arithmetic mean means the sum of the given data, divided by the total values of the set.

It may be a whole number or a decimal.

Mean means average.

In other words, AM is the sum of n numbers, divided by n.

If a1, a2, a3,...an are real numbers, their AM is defined as

 a1+a2+a3...+an n

Examples:

1. Find the Arithmetic mean of driving speed for 6 different cars 66mph, 57mph, 54mph, 69mph, 58mph, and 71mph.

Solution:

Sum of the given data = 66+57+54+69+58+71 = 375

=375/6 =62.5

2. Find the AM of -4,3,5,6,8

Solution:

Sum of the given numbers = -4+3+5+6+8 = 18

A.M =             18/5 =3.6

3. Insert four A.M s between -1 and 14.

Solution:

Let A1,A2,A3 and A4 be the four A.M s between -1 and 14.
By definition -1,A1,A2,A3 and A4,14 are in A.P and "d" be the common difference.
A1 = -1 + d,A2= -1 + 2d,A3= - 1 + 3d,A4 = -1 + 4d,A5 = - 1 + 5d
Here the value of A5 is 14.
-1 + 5 d = 14
Add 1 on both sides
-1 + 1 + 5d = 14 + 1
5d = 15
d = 15/5
d = 3

Generalization of the concept is the weighted arithmatic mean, also known as weighted average. Let w1, w2, w3, ...wn be numbers, whose sum is not zero, which will be known as weights, then the weighted mean of a1, a2,...an is defined to be

 w1a1+w2a2+...+wnan w1+w2+.....+wn

Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life. They are:

It subtracts sadness and adds happiness in our life.

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”