Question

What is the median of the first 10 natural numbers?

Answer 1

Hint: In this problem, we have to find the median of the first 10 natural numbers. We know that the first 10 natural numbers starting from 1 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. We know that the formula to find the median value is \[Median=\dfrac{{{\left( \dfrac{n}{2}+1 \right)}^{th}}term+{{\left( \dfrac{n}{2} \right)}^{th}}term}{2}\]. We can count the given number and substitute the n value to get the median of the first 10 natural numbers.

Complete step-by-step answer:
Here we have to find the median of the first 10 natural numbers.
We know that the first 10 natural numbers starting from 1 are
1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
 Here we can see that there are 10 numbers given
\[\Rightarrow n=10\]
Where the number of terms is in even.
We know that the formula to find the value of median whose n value is given,
\[\Rightarrow Median=\dfrac{{{\left( \dfrac{n}{2}+1 \right)}^{th}}term+{{\left( \dfrac{n}{2} \right)}^{th}}term}{2}\]
We can now substitute the value of n in the above formula, we get
\[\Rightarrow Median=\dfrac{\left( \dfrac{10}{2}+1 \right)+\left( \dfrac{10}{2} \right)}{2}\]
We can now simplify the above step, we get
\[\Rightarrow Median=\dfrac{6+5}{2}=\dfrac{11}{5}\]
We can now divide the above fraction, we get
\[\Rightarrow Median=\dfrac{11}{5}=5.5\]
Therefore, the median of the first 10 natural numbers is 5.5.

Note: We should always remember that the formula to find the median value with n number of terms is \[\Rightarrow Median=\dfrac{{{\left( \dfrac{n}{2}+1 \right)}^{th}}term+{{\left( \dfrac{n}{2} \right)}^{th}}term}{2}\]. We should also know that the natural numbers are the number system, which is from 1 to infinity.