# What is the average of the first nine prime numbers?

(A) $9$

(B)$11$

(C)$11\dfrac{1}{9}$

(D)$11\dfrac{2}{9}$

Last updated date: 21st Mar 2023

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Answer

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Hint: Specify the definition of prime numbers. Find the first nine prime numbers using the same and then find their average value. Average of nine prime numbers is the ratio of sum of prime numbers and total number of prime numbers.

Complete step-by-step solution -

Given the problem, we need to find the average of the first nine prime numbers.

First, we need to find the first nine prime numbers.

A prime number is a whole number larger than the number 1 that can be divided only by itself and 1.

A prime number has only two factors, 1 and the number itself.

From the above definitions, the first nine prime numbers are:

$2,3,5,7,11,13,17,19,23$

We need to find the average of the above prime numbers.

We know that average of n numbers is given by

${\text{Average Value}} = \dfrac{{{\text{Sum of n numbers}}}}{{\text{n}}}$

In the given problem, n=9.

The sum of first nine prime numbers obtained $ = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 = 100$

Hence the average value is given by

${\text{Average Value}} = \dfrac{{{\text{Sum of first nine prime numbers}}}}{9} = \dfrac{{100}}{9} = 11\dfrac{1}{9}$

Hence the average of nine prime numbers is $11\dfrac{1}{9}$.

Therefore, option (C). $11\dfrac{1}{9}$ is the correct answer.

Note: The formula of calculating average should be kept in mind while solving problems like above. The difference between prime numbers and composite numbers should be carefully understood for solving problems like above.

Complete step-by-step solution -

Given the problem, we need to find the average of the first nine prime numbers.

First, we need to find the first nine prime numbers.

A prime number is a whole number larger than the number 1 that can be divided only by itself and 1.

A prime number has only two factors, 1 and the number itself.

From the above definitions, the first nine prime numbers are:

$2,3,5,7,11,13,17,19,23$

We need to find the average of the above prime numbers.

We know that average of n numbers is given by

${\text{Average Value}} = \dfrac{{{\text{Sum of n numbers}}}}{{\text{n}}}$

In the given problem, n=9.

The sum of first nine prime numbers obtained $ = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 = 100$

Hence the average value is given by

${\text{Average Value}} = \dfrac{{{\text{Sum of first nine prime numbers}}}}{9} = \dfrac{{100}}{9} = 11\dfrac{1}{9}$

Hence the average of nine prime numbers is $11\dfrac{1}{9}$.

Therefore, option (C). $11\dfrac{1}{9}$ is the correct answer.

Note: The formula of calculating average should be kept in mind while solving problems like above. The difference between prime numbers and composite numbers should be carefully understood for solving problems like above.

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