Mathematics is soul of science. Most of the people take the decisions based on statistical analysis. And average the most common methodology to find most common answer from the given input value.
Many of the people, I find they making average of, average and new coming value. And find wrong answer.
For example, I want to make average of number 1, 2, answer will be 1.5. Now you get reading that is 3. Now to find average of this value few of researchers/scholars make average of 1.5 and 3
Average of Reading 1 and 2 = 1+2 = (3/2) = 1.5
Add new Value “3” to find New value; 1.5 +3 = (4.5/2) = 2.25
But actual average of 1, 2, 3 is (1+2+3)/3 = 2.
Now you get to value 2.25 and actual value is 2, you got a difference of 0.25.
This is the wrong methodology to find out of any reading. In these cases you want to find correct average here is the formula.
Is previously calculated average.
N is number of reading used to find previously average.
Nix is new value we are going to add in average.