Question

Find the median of the first ten prime numbers.

Answer 1

Hint: List the first ten prime numbers. They are already in ascending order, hence, choose the two middle numbers. Add them and divide by 2 to get the median.

Complete step-by-step answer:
Prime numbers are whole numbers greater than 1, which have only 1 and the number itself as the factors. Prime numbers are divisible only by the number 1 and itself.
Examples of prime numbers are 2, 3, 5, 7, and so on. 1 is neither prime nor a composite number.
The first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
The Median is the middle number in a given sequence sorted in ascending or descending order. To determine the median of a given sequence, we must arrange the given numbers in ascending or descending order.
If the total number of numbers in the sequence is odd, the median is the middle number. If the total number of the numbers in the sequence is even, then we will have two middle numbers. The median is the average of these two numbers.
We have the sequence:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
It is already in ascending order, so we find the middle numbers.
There are 10 numbers, hence, the 5th and the 6th numbers will be the middle numbers.
Hence, the middle numbers are 11 and 13.
Now, the average of 11 and 13 is given as follows:
Average of 11 and 13 = \[\dfrac{{11 + 13}}{2}\]
Average of 11 and 13 = \[\dfrac{{24}}{2}\]
Average of 11 and 13 = 12
Hence, the median of the first ten prime numbers is 12.

Note: You might miss the number 19 when writing the prime numbers. Remember that 19 is also a prime number. When we have an even number of terms, we need to take the average of the middle numbers and not choose any one of them.