Question

Median of first $50$ even natural numbers is ______________

Answer 1

Step1: Given:

First $50$ even natural numbers, that is, $n=50$

First $50$ even natural numbers are $2,4,6,8,10,.............,48,50,52,54,............,98,100$

Step2: Formula to find Median when $n$ is even

Median $=\frac{{\displaystyle \frac{n}{2}}thterm+({\displaystyle \frac{n}{2}}+1)thterm}{2}$

Substitute the value of $n=50$

Median $$\begin{gathered} =\frac{{\displaystyle \frac{50}{2}}thterm+({\displaystyle \frac{50}{2}}+1)thterm}{2} \\ =\frac{{25}^{th}term+{26}^{th}term}{2} \end{gathered}$$

As, we can see that first term, $2=2\times 1$, second term,$4=2\times 2$ so on therefore, $n^{th}term=n\times 2=2n$.

$\therefore {25}^{th}term=25\times 2=50and{26}^{th}term=26\times 2=52$

Substitute the values in the formula to get the answer

$$\begin{gathered} Median=\frac{50+52}{2} \\ =\frac{102}{2} \\ =51 \end{gathered}$$

Final answer Hence, the median of first $50$even natural numbers is $51$.