Question

What is the Arithmetic Mean of the first 5 whole numbers?
 $ \begin{align}
  & \text{a) 1} \\
 & \text{b) 2} \\
 & \text{c) 3} \\
 & \text{d) 5} \\
\end{align} $

Answer 1

Hint: Now in the given question we are given the first 5 whole numbers and we have to find their Arithmetic Mean. Arithmetic mean is simply the mean or average of given data which are in Arithmetic progression. The whole number starts from 0. Hence the whole numbers are listed as 0, 1, 2 …
Hence we will calculate the average of the numbers 0, 1, 2…4. i.e. the first five whole numbers.

Complete step-by-step answer:
Now the whole numbers are 0, 1, 2 …
Hence, the first 5 whole numbers are 0, 1, 2, 3, and 4.
Now, $ 1-0=2-1=3-2=4-3=1 $ .
This means the difference between each successive two terms is 1.
Hence we know that the numbers 0, 1, 2, 3 and 4 are in Arithmetic progression with common difference equal to 1.
We know that the arithmetic mean of $ {{x}_{1}},{{x}_{2}},{{x}_{3}},{{x}_{4}}...{{x}_{n}} $ is given by $ \dfrac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}+...{{x}_{n}}}{n} $
Now the Arithmetic mean of these numbers will be the sum of numbers divided by number of terms.
The sum of the numbers is equal to $ 0+1+2+3+4=10 $ .
And the number of these terms are 5.
Now let A be the Arithmetic mean of 0, 1, 2, 3 and 4.
Hence the value of A will be
 $ A=\dfrac{0+1+2+3+4}{5}=\dfrac{10}{5}=2 $ .
Hence we get the Arithmetic mean of the given numbers is 2.
So, the correct answer is “Option B”.

Note: We should keep in mind that the Whole numbers start from 0 and not to be confused with Natural numbers which start from 1. Hence while considering the Numbers start from 0.