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$ \begin{align}

& \text{a) 1} \\

& \text{b) 2} \\

& \text{c) 3} \\

& \text{d) 5} \\

\end{align} $

Answer
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Hence we will calculate the average of the numbers 0, 1, 2…4. i.e. the first five whole numbers.

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.