The median of first 10 prime numbers will be

Options

A. 5
B. 11
C. 12
D. 13

Answer

To find the median of the first 10 prime numbers, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the First 10 Prime Numbers**:
The first 10 prime numbers are:
\[ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 \]

2. **Count the Number of Observations**:
We have a total of 10 prime numbers. Since 10 is an even number, we will use the formula for finding the median in a dataset with an even number of observations.

3. **Use the Median Formula**:
The formula for the median when the number of observations (N) is even is:
\[ \text{Median} = \frac{\text{(N/2)th term} + \text{((N/2) + 1)th term}}{2} \]
Here, \( N = 10 \).

4. **Calculate N/2 and (N/2) + 1**:
\[ N/2 = 10/2 = 5 \]
\[ (N/2) + 1 = 5 + 1 = 6 \]

5. **Find the 5th and 6th Terms**:
From our list of prime numbers:
- The 5th term is \( 11 \).
- The 6th term is \( 13 \).

6. **Calculate the Median**:
Now, substitute the 5th and 6th terms into the median formula:
\[ \text{Median} = \frac{11 + 13}{2} = \frac{24}{2} = 12 \]

7. **Conclusion**:
The median of the first 10 prime numbers is \( 12 \).