Question

Find the median of the first ten whole numbers?

Answer 1

Hint: We start solving the problem by recalling the definition of whole numbers and writing the first 10 whole numbers using this definition. We then recall the fact that median of ‘n’ even terms that were written in ascending order is equal to the average of the ${{\left( \dfrac{n}{2} \right)}^{th}}$ and ${{\left( \dfrac{n}{2}+1 \right)}^{th}}$ terms. We then check what these terms are from the first 10 whole numbers and take the average of them to get the required median.

Complete step by step answer:
According to the problem, we need to find the median of the first ten whole numbers.
Let us recall what are whole numbers. We know that the whole numbers start with 0 and move to the right side of the number line having only positive numbers other than 0.
So, the set of numbers containing whole numbers is defined as $\left\{ 0,1,2,3............. \right\}$.
Using this definition, we get the first ten whole numbers as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
We know that the median of the ‘n’ even terms that were written in ascending order is equal to the average of the ${{\left( \dfrac{n}{2} \right)}^{th}}$ and ${{\left( \dfrac{n}{2}+1 \right)}^{th}}$ terms.
We have $n=10$ here. So, the median is equal to the average of the ${{\left( \dfrac{10}{2} \right)}^{th}}={{5}^{th}}$ and \[{{\left( \dfrac{10}{2}+1 \right)}^{th}}={{6}^{th}}\] terms.
From the first 10 whole numbers, we can see that ${{5}^{th}}$ and ${{6}^{th}}$ terms are 4 and 5.
So, let us find the average of the terms a and b is $\dfrac{a+b}{2}$.
We get the average of 4 and 5 as $\dfrac{4+5}{2}=\dfrac{9}{2}=4.5$.
So, we have found the median of the first 10 whole numbers as 4.5.

∴ The median of the first 10 whole numbers is 4.5.

Note: We should make sure that the terms have to be written in ascending order before finding the median of any number of terms. As we know that the whole numbers will always be increasing in nature we don’t need to check again for this problem. We should make sure whether the total number of terms are even or odd. If the total no. of terms are odd, then we get only one term as median.