The arithmetic mean of the direct 100 natural numbers is
A. 55.2
B. 60.1
C. 25.7
D. 50.5
Answer: Option D
Solution (By Examveda Team)
Understanding the Question:This question asks you to find the average (arithmetic mean) of the first 100 natural numbers. Natural numbers are the counting numbers: 1, 2, 3, and so on.
Finding the Arithmetic Mean:
The arithmetic mean is calculated by adding all the numbers together and then dividing by the total number of numbers. In this case, we need to add up the numbers from 1 to 100, and then divide by 100.
A Simple Trick:
There's a shortcut! To find the sum of numbers from 1 to 100, you can use the formula: (n * (n + 1)) / 2, where 'n' is the last number (100 in this case).
Let's calculate:
1. Substitute n = 100 into the formula: (100 * (100 + 1)) / 2 = (100 * 101) / 2 = 5050
2. Divide the sum (5050) by the total number of numbers (100): 5050 / 100 = 50.5
Therefore, the arithmetic mean of the first 100 natural numbers is 50.5.
The correct answer is D: 50.5
This Question Belongs to Home Science >> Extension Management And Community Development
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Solution-n(n+1)÷2
=100(100+1)÷2
=101÷2
=50.5