Question

Find the mean of all prime numbers between \[20\] and \[40\].

Answer 1

Hint: We have to find the value of the mean of the prime numbers between \[20\] and \[40\]. We will solve this question using the concept of prime numbers and the concept of mean of numbers. First we will find all the prime numbers between \[20\] and \[40\]. Then we will find the value of the mean of the prime numbers by using the formula as the sum of all the prime numbers upon the total number of prime numbers between \[20\] and \[40\].

Complete step-by-step solution:
Given :
To find the mean of all the prime numbers between \[20\] and \[40\].
As,we know that all the prime numbers between \[20\] and \[40\] are as follows :
\[23\],\[29\],\[31\],\[37\].
Now,we know that the formula of mean of \[n\] terms is given as :
\[mean = \dfrac{{{x_1} + {x_2} + {x_3} +................... + {x_n}}}{n}\]
[Where \[n\] is the number of terms of the data]
So,using the formula of mean as stated above we can calculate the mean of the prime numbers between \[20\] and \[40\] as :
\[mean = \dfrac{{23 + 29 + 31 + 37}}{4}\]
On solving the above expression,we get
\[mean = \dfrac{{120}}{4}\]
On further solving,we get the value of the mean of all the prime numbers between \[20\] and \[40\] as :
\[mean = 30\]
Hence,the mean of all the prime numbers between \[20\] and \[40\] is \[30\].

Note: The formula of mean of n number of terms is given as : the sum of the value of the \[n\] observations upon the total number of observations or simply the number of terms. This formula can be only used for single number data,such as the marks of students in a class, the height of students in a college etc. We have different formulas for different values of the data.