Question

What is the median of the first five natural numbers?

Answer 1

Hint: The set of natural numbers is $ \mathbb{N}: = \{ 1,2,3,4,5,...\} $ and the first five natural numbers are $ 1,2,3,4,5 $ . The first step of finding the median of a data is to arrange all the terms of the data in ascending order. We will arrange the natural numbers in ascending order and then number them and use the formula for median. After doing this much we will be getting our answer.

Complete step-by-step answer:
If \[{x_1},{x_2},...{x_n}\] are $ n $ data then median is given by the formula:
 $ M = \dfrac{n}{2} $ , if $ n $ is even
 $ M = \dfrac{{n + 1}}{2} $ , if $ n $ is odd
We have to find the median of the first five natural numbers.
The first five natural numbers are $ 1,2,3,4,5 $ .
The data given in our question has five entries so we can list them out as:
 $ {x_1} = 1 $
 $ {x_2} = 2 $
 $ {x_3} = 3 $
 $ {x_4} = 4 $
 $ {x_5} = 5 $
Clearly, we have $ n = 5 $ which is an odd number so we will use the formula for finding median in case of
Odd number of data.
So,
 $ \Rightarrow M = \dfrac{{5 + 1}}{2} = \dfrac{6}{2} = 3 $
Thus, the median is the third-term.
The third term in our case is $ {x_3} = 3 $ .
Therefore, the median of the first five natural numbers is $ 3 $ .

Note: An alternative way of doing this is by just using hit and trial method. By the definition of median it is the middlemost entry of a data .So after arranging the data in sequence of ascending order we can check which is the middle most element. We can see that $ 3 $ has two elements above it and two elements below it, which makes it ideal to be the median of our given data.