Did You Know These Facts About Average Of Numbers

 

In our classes teacher teaches us that average of n number is given as

And this is only about average. But this is not fare with average concept. Here, I give you some basic understanding and some concept related to numbers.

First thing I cleared here that average is a tool which help us to see a broader picture of many problem or solution .Some key words that you must here in your daily life that average internet connection speed, Average income of a family, etc.

Wikipedia said that an average is a single number taken as representative of a list of numbers.

This is a different view of seeing average beside of its formulae. With the help of average you can say many things about its entries which are used in average. I know these things are not in your books but you have to think these things to yourself. And here I give you a way how to think?

Take a example, if average of 10 numbers is 1 then what you can say about these ten numbers. What that 10 number be? For this come on the mathematical form.

         

=   a1+a2+a3+………..+a10 = 10

From above it is clear that the sum of that 10 numbers is 10, if average is 1. If entry is whole number then a1, a2, a3 ………, a10 ≤ 10. Which means that entries lies between 1 to 10. Not only this, but you can say more about these entries. If a single number is equals to 10 then all other are necessarily equals 0. Similarly, if a entry is equals to 5 then other all entries are less then or equals to 5. Similarly, for other possibilities.

Now the last but not the least, What is the basic difference between Average and Arithmetic mean. This question arises here because average of two numbers is 

 and Arithmetic mean is same. Then what is difference between them?

Arithmetic mean is only defined for special kind of progression called Arithmetic progression in which difference between any two consecutive entries is same.

So, if a₁ ,a₂ , a₃ ,…..a_n  are in Arithmetic progression then arithmetic mean of a₁ and a₃ gives a₂ and arithmetic mean is calculated only when the series is  in Arithmetic progression. But Average is calculated for ant number and no need of any special progression.

Many more concepts are hidden inside the formulae and definition.Some of them are written in books and some of them you have to think your self.

Thank you.

S.K. Ojha