Question

Find the average of all prime numbers between $60$ and $90$.
A. $72$
B. $74.7$
C. $74$
D. $73.6$

Answer 1

Hint: In this problem, to find an average first we will write all prime numbers between $60$ and $90$. Then, we will find the sum of all those prime numbers. If there are $n$ prime numbers then to find an average we will divide the sum of all those prime numbers by $n$.

Complete step-by-step solution:
To find an average, first we will write all prime numbers between $60$ and $90$. The prime numbers between $60$ and $90$ are $61,67,71,73,79,83,89$. We can see that there are $7$ prime numbers between $60$ and $90$.
Let us find the sum of all these prime numbers. Therefore, we get $61 + 67 + 71 + 73 + 79 + 83 + 89 = 523$.
To find an average, we will divide this sum $523$ by $7$ because there are $7$ prime numbers. Therefore, we get average value $ = \dfrac{{523}}{7} = 74.7$.
Therefore, we can say that the average of all prime numbers between $60$ and $90$ is $74.7$.

Hence the correct answer is option B is true.

Note: If the number has only two factors, $1$ and a number itself, then we can say that the number is prime. The smallest even prime number is $2$. Note that there is only one even prime number. Let us see how to find all prime numbers between $60$ and $90$. We know that all even numbers between $60$ and $90$ are not prime. The odd numbers between $60$ and $90$ are $61,63,65,67,69,71,73,75,77,79,81,83,85,87,89$. Now we will eliminate the multiples of $3$. That is, we will eliminate $63,69,75,81,87$. Then, we will eliminate the multiples of $5$. That is, we will eliminate $65,85$. Then, we will eliminate the multiples of $7$. That is, we will eliminate $77$. Therefore, we get $61,67,71,73,79,83,89$. These are all prime numbers between $60$ and $90$. If the number is not prime then we can say that it is a composite number.