Question

Which of the following is the mean of prime numbers between 20 and 30.
A. 21
B. 26
C. 25
D. 27

Answer 1

Hint: To find the mean of prime numbers between 20 and 30, we should find the prime numbers between these numbers. Prime numbers are the numbers that have only 2 factors: 1 and themselves. Hence, we get the prime numbers as 23 and 29. Now, we will use the equation $\text{Mean=}\dfrac{\text{Sum of given data}}{\text{Total number of data}}$ . We know that total number data is 2. Hence, by substituting the values in the formula, the required mean can be calculated.

Complete step-by-step answer:
We need to find the mean of prime numbers between 20 and 30. Let us first see what prime numbers are.
Prime numbers are the numbers that have only 2 factors: 1 and themselves.
Now, let us see the prime numbers between 20 and 30. Let us find factors of numbers between 20 and 30.
We know that the factors of 20 = 1,2,4,5,10
For 21, we have the factors as 1,3,7,21
We know that the factors of 22 = 1,2,11,22
For 23, we have 1,23
We have the factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
25 has factors as 1,5,25
We have the factors of 26 = 1, 2, 13, 26
The factors of 27 are 1, 3, 9, 27
For 28, we have the factors as 1, 2, 4, 7, 14, 28
We know that the factors of 29 = 1, 29
We can write the factors of 30 as 1, 2, 3, 5, 6, 10, 15, 30
From the above data, we can see that the prime numbers are 23 and 29.
Now, let us find the mean.
Mean is given by,
$\text{Mean=}\dfrac{\text{Sum of given data}}{\text{Total number of data}}$
Let us find the total number of data.
Total number of data = Number of prime numbers = 2
Hence, we can substitute the values as
$\begin{align}
  & \text{Mean=}\dfrac{\text{23+29}}{\text{2}} \\
 & =\dfrac{52}{2} \\
 & =26 \\
\end{align}$

So, the correct answer is “Option B”.

Note: There can be an error when finding the total number of data. Do not take 10 as this value as we find the prime numbers between 20 and 30. Total number of data is the number of observations, in other words, total number of prime numbers.