Question

The mean of the first five prime numbers is
A) 5.6
B) 3.6
C) 6.83
D) 5.2

Answer 1

Hint: First, we will begin by writing the first five prime numbers, which are 2, 3, 5, 7, and 11. After that calculate the sum of these whole numbers. Then use the mean formula $\bar x = \dfrac{{\sum {{x_i}} }}{n}$ and do simplification to find the mean of the first five whole numbers.

Complete step-by-step solution:
Prime numbers are considered as the numbers which retain only two factors i.e. one and itself. It implies that the number can be divided only by 1 and itself. All prime numbers are an odd number apart from 2.
So, the first five prime numbers are 2, 3, 5, 7, and 11.
We have to find the mean of the first five prime numbers.
The mean is calculated by dividing the sum of observations by the number of observations. The formula is given by,
$\bar x = \dfrac{{\sum {{x_i}} }}{n}$
We will find the sum of observations by adding all the first five prime numbers.
$ \Rightarrow \sum {{x_i}} = 2 + 3 + 5 + 7 + 11$
Add the terms on the right side,
\[ \Rightarrow \sum {{x_i}} = 28\]
Now, substitute the value in the mean formula,
$ \Rightarrow \bar x = \dfrac{{28}}{5}$
Divide the numerator by denominator,
$\therefore \bar x = 5.6$
So, the mean of the first five prime numbers is 5.6.

Hence, option (A) is correct.

Note: Whenever we face such types of problems the key point that we need to recall is that Mean or Arithmetic mean is the average of given numbers. It is found by calculating the sum of the given numbers and dividing it by how many numbers there are. These types of questions are based only on this definition and can be easily solved using this.