PROBLEMS ON AVERAGE - 1

Examples 1: what will be the average of 11, 12, 13, 14, 15, 16, 17 series?

Solution: The common difference is same i.e., 1, so the series is in A.P. Average is the middle term when the number of terms is odd, So the middle term is 14 which is our average of the series.

Example 2: What will be the average of 11, 12, 13, 14, 15, 16, 17, 18?

Solution: Since the common difference is same for each of the term we can say that the series is in A.P. So we have discussed that when the number of terms are even then the average will be the average of two middle terms.

Now the two middle terms are 14 and 15, and the average is (14+15)/2 = 14.5

Example 3: The average of five numbers is 29. If one number is excluded the average becomes 27. What is the excluded number ?

Solution: let the excluded number is

= (29 x 5) – ( 27 x 4 )

= 145 – 108

= 37 .

Example 4: Find the average of first 20 natural numbers?

Solution: 

Sum of first n natural numbers = n ( n + 1 ) /2

So, we can find easily average of first 20 natural numbers 20 x 21 / 2 = 210 

So, then Required average is = 210 / 20 = 10.5.

Example 5 : Find the average of first 20 multiplies of 5 .

Solution: 

Required average = 5 ( 1 + 2 + 3 +……………….. + 20) /20

= ( 5 x 20 x 21 / 20 x 2) = 2100 / 40 = 52.5 .

So the Required average is 52.5.