Question

The mean of first five prime numbers is
A. \[3\]
B.\[3.6\]
C.\[7\]
D.\[5.6\]

Answer 1

Hint:Here we use the definition of prime numbers and find the first 5 prime numbers. Using the formula for the mean of numbers we calculate the mean of the first 5 prime numbers.

Complete step-by-step answer:
Prime numbers are the numbers which are only divisible by 1 and the number itself. So p is said to be a prime number if it has no other factor than 1 and p. Examples: 13, 7 etc.
Mean is the average value which can be calculated by dividing the sum of observations by number of observations.
We have to find the mean of the first five prime numbers.
From the definition of prime numbers we can write prime numbers in ascending order as 2, 3, 5, 7 and 11.
Now we calculate the sum of first five prime numbers
\[ \Rightarrow \]Sum \[ = 2 + 3 + 5 + 7 + 11\]
\[ \Rightarrow \]Sum \[ = 28\]
Also, we know the number of observations is 5 because we are calculating the mean of the first 5 prime numbers.
We know the mean of n observations is the sum of n observations divided by n.
\[ \Rightarrow \]Mean \[ = \dfrac{{28}}{5}\]
Calculate the fraction by dividing 28 by 5
\[ \Rightarrow \]Mean \[ = 5.6\]
Therefore, mean of first five prime numbers is 5.6

So, the correct answer is “Option D”.

Additional Information:The numbers which are not prime numbers are called composite numbers. Composite numbers have factors other than 1 and the number itself.

Note:Students many times make the mistake of considering 1 as a prime number because it has only one factor that is 1. Keep in mind that 1 is neither a composite number nor a prime number so we start our observations from 2.