Average: Notes, Concept & Shortcut (Quantitative Aptitude) Part 2

An average or more accurately an arithmetic mean is term as the sum of a number of data divided by n(term). 

Average= Sum of all numbers/ total number of terms

Example1- An average of 31, 37, 41, 43, and 47
Method 1- Basic method
Sum of all the number=199
Number of terms= 5

Average= 199/5=39.8

Note: The average is equal distribution of each number

Method2- Divergence method 

We know the average is mean

You choose any number as an average

Let select- 41 as an average
Now compare every number with the assumed averag
31, 37, 41, 43, 47
31 is 10 less than 41
37 is 4 less than 41
43 is 2 more than 41
47 is 6 more than 41
Deviation=(-10-4+2+6)=-6
-6 is divided into a number of terms
= -6/5=-1.2
Subtract from the average we assume= 41-1.2=39.8

So the formula for deviation

New average= Old average+deviation/number if terms)

Above method is very helpful in Data Interpretation 

Example 2- Average of 2014, 2019, 2025, 2030, 2050
Select the median value I.e 2000
Since all number are stating from 2000 so
Deviation= 14+19+25+30+50=138
New average= 2000+138/5=2027.6

Let say number are 49, 25, 16, 10
Here average is=sum of number/total number of term
 49+25+16+10=100/4=25
That means each value is equal to 25

Some value left

Now-case 1- If 25 goes from the number no change in average

Case2- When 49 goes what is the change in average

We know the average is 25, 49 are 24 more than the average
49 goes it take 24 from the given term so 24 is divided into 3 remaining number
24/3=8 so it takes 8 from the average of each number
Now the average is 25-8=17

Case3-when 16 goes from the number
16 is 9 less than from 25, so there is a surplus of 9
This 9 is distributed to remaining term= 9/3=3
Now the average is 28.

Some value come 

Case 4- Now say one number comes
49, 25, 16, 10
Say if 35 comes
We know an average number is 25
35 is 10 more than the average
Now there is a surplus of 10, this 10 is equally distributed among the number of terms so the average is 27.

Some Basic Formula
Average of n natural number= (n+1)/2
Average of n even number=(n+1)
Average of n odd number= n
Average of n consecutive natural number= (First number + Last number)/2