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 will follow these steps:

### Step 1: Identify the first 10 prime numbers.
The first 10 prime numbers are:
1. 2
2. 3
3. 5
4. 7
5. 11
6. 13
7. 17
8. 19
9. 23
10. 29

### Step 2: Determine the number of observations.
We have identified that there are 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.

### Step 3: Use the median formula for even numbers.
The formula for finding the median when the number of observations (n) is even is:
\[ \text{Median} = \frac{(n/2)^{th} + ((n/2) + 1)^{th}}{2} \]
In our case, \( n = 10 \).

### Step 4: Calculate the positions for the median.
We calculate:
- \( n/2 = 10/2 = 5 \)
- \( (n/2) + 1 = 5 + 1 = 6 \)

### Step 5: Find the 5th and 6th prime numbers.
From our list of prime numbers:
- The 5th prime number is 11.
- The 6th prime number is 13.

### Step 6: Calculate the median.
Now we can substitute these values into the median formula:
\[ \text{Median} = \frac{11 + 13}{2} = \frac{24}{2} = 12 \]

### Final Answer:
The median of the first 10 prime numbers is **12**.

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