Question

Find the median of first $10$ odd prime numbers.

Answer 1

Hint: The median is the middle number in a list of numbers ordered from lowest to highest. So, we arrange the list of the first ten odd prime numbers. Prime numbers are numbers which can be divided exactly only by itself and $1$. Except for $1$ which is neither prime nor composite.

Complete step-by-step answer:

Following this rule for prime numbers, the prime numbers are : $2\text{, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37,41,}....$and so on.

 Now, an odd number is a number which is not divisible by $2$.

So, odd numbers are $\text{3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37,41}$. Clearly, only $2$ is a number which is even and prime. After that there is no prime number which is even as well as prime. Because if a prime number is even other than $2$ then it is divisible by $2$. So, it is divisible by itself, $2$ and $1$. So, it fails the definition of prime that a prime number will be prime only and only if it is divisible by itself and $1$. Hence, all numbers other than $2$ are odd prime.

So, the first 10 odd prime numbers are as follows $3,\text{ 5, 7, 11, 13,17, 19, 23, 29, 31}$.
Now, to find median what we do

Case – 1st

In a list of even numbers arranged in order.

                                    Median $=$ middle term

Case – 2nd

In list of odd number of numbers arranged in order

                                Median $=$ average of two middle most number

So, here in the list $\left( 3,\text{ 5, 7, 11, 13,17, 19, 23, 29, 31} \right)$. $13$ and $17$ are middle most.

So, their average $=\dfrac{13+17}{2}=10$

So, median of the list $=10$

So, the median of the first 10 odd prime numbers is $10$.

Note: One may include $1$ in the list thinking it to be prime. But $1$ is neither prime nor composite. Further, one should not select either of $13$ or $17$ but should take average of it.