Question

we can find out the relation between consecutive natural numbers and their average​

Answer 1

Average is the sum of the data values divided by the total number of data values.

Given that, average of 5 consecutive natural numbers is m

Let the 5 consecutive natural be (x−2),(x−1),x,(x+1),(x+2)

Therefore, average is  

5

(x−2)+(x−1)+x+(x+1)+(x+2)

​  

 

⟹m=  

5

5x

​  

⟹x=m -------(1)

Given that next three natural numbers are included. Therefore, the next three natural numbers will be (x+3),(x+4),(x+5)

Therefore, the average of all the 8 numbers  

=  

8

(x−2)+(x−1)+x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)

​  

 

=  

8

8x+12

​  

 

=x+  

8

12

​  

 

=m+1.5   (from (1))

Therefore the average of the 8 numbers is 1.5 more than m