Question

The mean of the first ten prime numbers is.
A. 12
B. 12.9
C. 13
D. 14

Answer 1

Hint: We will write the first ten prime numbers and then will add them to find their sum. We will then substitute the values in the formula of mean , which is, ${\text{Mean}} = \dfrac{{{\text{Sum of observations}}}}{{{\text{Number of observations}}}}$ to get the required answer.

Complete step-by-step answer:
We have to find the mean of the first ten prime numbers.
Prime numbers are the numbers that have only two factors, the number 1 and the number itself.
The first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29
Mean is calculated by adding all the observations by the total number of observations.
The formula of mean is $\dfrac{{{\text{Sum of observations}}}}{{{\text{Number of observations}}}}$
Therefore, we will calculate the sum of the first ten prime numbers.
$
   \Rightarrow 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 \\
   \Rightarrow 129 \\
$
Now, we will divide this by 10 as there are a total 10 numbers.
$\dfrac{{129}}{{10}} = 12.9$
Hence, the mean of first ten prime numbers is 12.9
Thus, option B is correct.

Note: Mean is also known as average. 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.