Question

Find the average of the first four prime numbers.
A. 4
B. 4.25
C. 5
D. 6.25

Answer 1

Hint: We first define the concept of prime numbers. We use examples for both prime and non-prime numbers to find out the differences. Then we find the first four prime numbers. Then using the law of average, we find the solution of the problem.

Complete step by step answer:
Now the concept of prime number comes from the concept of divisibility.
If a natural number is divisible by only 1 and itself then the number is called a prime number. So, prime numbers will always have exactly 2 divisors. Any other natural number other than prime numbers are called non-prime numbers. They will definitely have a divisor other than 1 and that number itself. So, the number of divisors is greater than 2.
For example: we take 17. This number is only divisible by 1 and 17. So, 17 is a prime number.
And we take 8. It’s divisible by 1, 2, 4, 8. So, this is a non-prime number.
Exceptional case being 2. Although it’s an even number, due to its position in natural number series it has no lesser number other than 1 which divides it. So, due to the lack of numbers it became a prime number. Also, we need to remember 1 is neither a prime nor a non prime number.
Now we find the first four prime numbers.
It starts with 2. Then 3 is also a prime number as 3 is only divisible by 1 and 3.
4 being an even number it can’t be prime. So, the next prime number is 5 which is only divisible by 1 and 5.
The next prime number is 7.
So, the numbers are 2, 3, 5, 7.
Now we need to find the average of those numbers.
Average is division of the sum by the number of terms.
Here the sum of the numbers is $2+3+5+7=17$. Total number of terms is 4.
So, the average is $\dfrac{17}{4}=4.25$.
The correct option is (B).
Note:
We need to be careful about 2 being a prime number. Although 2 is even, it’s the only even number that is prime. It’s prime because of its position in natural number series. It got no lesser number other than 1 which divides it.