Question

Find the mean of the first five prime numbers.
A. 3.3
B. 7.8
C. 5.6
D. 12.1

Answer 1

Here in this problem we have to find out the mean of the first five numbers. First we have to know what prime numbers are, they are the numbers which are not divisible by any number, such kinds of numbers are called prime numbers. Mean is a statistical value which is also known as the average of the given set of observations, which is obtained by the ratio of the sum of observations to the total no. of observations.

Complete step-by-step solution:
The prime numbers are the numbers which are not divisible by any of the numbers.
For example: 2, 3, 5, 7, 11, 13, 17, 19,…….etc. , are prime numbers as they are not divisible by any of the numbers.
Here the first five prime numbers are given by :
$\Rightarrow 2,3,5,7,11$
Mean is the average of the observations, which is given by the ratio of the sum of the observations to the total no. of observations, as given below:
$\Rightarrow \dfrac{{\sum\limits_i {{x_i}} }}{n}$ , where $n$ is the total no. of observations, and ${x_i}$ denotes each observation for $i = 1,2,3,....n$
Now calculating the mean of the first five prime numbers.
The no. of observations here is 5.
$\therefore n = 5$
$\Rightarrow {x_1} = 2$
$\Rightarrow {x_1} = 3$
$\Rightarrow {x_1} = 5$
$\Rightarrow {x_1} = 7$
$\Rightarrow {x_1} = 11$
The mean of the first five prime numbers is given by:
$\Rightarrow \dfrac{{\sum\limits_{i = 1}^5 {{x_i}} }}{5} = \dfrac{{{x_1} + {x_2} + {x_3} + {x_4} + {x_5}}}{5}$
$\Rightarrow \dfrac{{\sum\limits_{i = 1}^5 {{x_i}} }}{5} = \dfrac{{2 + 3 + 5 + 7 + 11}}{5}$
$\Rightarrow \dfrac{{\sum\limits_{i = 1}^5 {{x_i}} }}{5} = \dfrac{{28}}{5}$
$\therefore \dfrac{{\sum\limits_{i = 1}^5 {{x_i}} }}{5} = 5.6$
The mean of first five prime numbers is 5.6

Option C is the correct answer.

Note: Note that here while considering the first five prime numbers you may think of starting with 1, which is not a prime number because it is divisible by 1. So 1 is neither prime nor composite.