What is the average of the first nine prime numbers?
(A) $9$
(B)$11$
(C)$11\dfrac{1}{9}$
(D)$11\dfrac{2}{9}$
Answer
688.5k+ views
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.
Recently Updated Pages
What is BLO What is the full form of BLO class 8 social science CBSE

Explain the Treaty of Vienna of 1815 class 10 social science CBSE

10 examples of friction in our daily life

Draw a diagram of nephron and explain its structur class 11 biology CBSE

Write structures of the following compounds i 2 Chloro3methylpentane class 11 chemistry CBSE

A Paragraph on Pollution in about 100-150 Words

Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Name 10 Living and Non living things class 9 biology CBSE

What is the full form of pH?

What is pollution? How many types of pollution? Define it

On an outline map of India show its neighbouring c class 9 social science CBSE

