Question
Find the median of first $10$ even numbers.
✓
Answer
First $10$ even numbers are $2, 4, 6, 8, 10, 12, 14, 16, 18, 20$
Here, number of terms $= 10$
which is even $\therefore\ \text{Median}=\frac{1}{2}\Big\{\frac{\text{n}}{2}\text{th term}+\Big(\frac{\text{n}}{2}+1\Big)\text{th term}\Big\}$
$=\frac{1}{2}\Big\{\frac{10}{2}\text{th term}+\Big(\frac{\text{10}}{2}+1\Big)\text{th term}\Big\}$
$=\frac{1}{2}\{5\text{th term}+6\text{th term}\}$
$=\frac{1}{2}(10+12)=\frac{1}{2}\times22=11$
Here, number of terms $= 10$
which is even $\therefore\ \text{Median}=\frac{1}{2}\Big\{\frac{\text{n}}{2}\text{th term}+\Big(\frac{\text{n}}{2}+1\Big)\text{th term}\Big\}$
$=\frac{1}{2}\Big\{\frac{10}{2}\text{th term}+\Big(\frac{\text{10}}{2}+1\Big)\text{th term}\Big\}$
$=\frac{1}{2}\{5\text{th term}+6\text{th term}\}$
$=\frac{1}{2}(10+12)=\frac{1}{2}\times22=11$
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