Question

i. Find the mean of natural numbers from 1 to 100.

ii. What is the mean of even numbers from 1 to 100? What is the mean of odd numbers?

iii. What is the difference between the means of the first 100 even numbers and odd numbers?

iv. What is the difference between the means of the first 200 even numbers and 200 odd numbers?

Answer 1

Sum of the natrural numbers from 1 to n = \(\frac{n}{n+1}2\)

Sum of the first 100 odd numbers

= 1002 = 100 × 100

In general, the difference between the means of n even numbers and n odd numbers is always 1.