Question

Find the arithmetic mean of the first five prime numbers.

Answer 1

We will write the first five prime numbers and then add them to find their sum. We will then substitute the values in the formula of arithmetic mean , $\dfrac{{{a_1} + {a_2}... + {a_n}}}{n}$, where $n$ is the number of terms and ${a_1},{a_2},..{a_n}$ are $n$ observations.

Complete step-by-step answer:
We have to find the arithmetic mean of the first five prime numbers.
Prime numbers are the numbers that have only two factors.
The first five prime numbers are 2, 3, 5, 7 and 11.
Arithmetic mean is calculated by adding all the observations by the total number of observations.
Arithmetic mean is given by $\dfrac{{{a_1} + {a_2}... + {a_n}}}{n}$, where $n$ is the number of terms and ${a_1},{a_2},..{a_n}$ are $n$ observations.
Therefore, we will calculate the sum of the first five prime numbers.
$\Rightarrow 2 + 3 + 5 + 7 + 11 \\\ \Rightarrow 28 \\\$
Now, we will divide this by 5 as there are a total 5 numbers whose arithmetic mean is to be calculated.
$\dfrac{{28}}{5} = 5.6$
Hence, the arithmetic mean of first five prime numbers is 5.6

Note: Arithmetic mean is also known as average or simply mean. Also, many students consider all odd numbers as prime numbers but there are odd numbers which are not prime. For example, 9 is an odd number and has 3 factors, 1, 3 and 9, and hence not a prime number. The number 1 is neither a prime nor a composite number.