The average of first nine prime numbers is:

Options

A. 9
B. 11
C. `11 (2/9)`
D. `11(1/9)`

Answer

To find the average of the first nine prime numbers, we will follow these steps:

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

### Step 2: Calculate the sum of these prime numbers.
Now, let's add these numbers together:
- 2 + 3 = 5
- 5 + 5 = 10
- 10 + 7 = 17
- 17 + 11 = 28
- 28 + 13 = 41
- 41 + 17 = 58
- 58 + 19 = 77
- 77 + 23 = 100

So, the sum of the first nine prime numbers is **100**.

### Step 3: Determine the number of observations.
The number of observations (prime numbers) we have is **9**.

### Step 4: Calculate the average.
The average is calculated by dividing the sum by the number of observations:
\[ \text{Average} = \frac{\text{Sum}}{\text{Number of Observations}} = \frac{100}{9} \]

### Step 5: Simplify the average.
When we divide 100 by 9, we get:
- 100 ÷ 9 = 11 with a remainder of 1, which can be expressed as:
\[ 11 \frac{1}{9} \]

Thus, the average of the first nine prime numbers is **11 1/9**.

### Final Answer:
The average of the first nine prime numbers is **11 1/9**.

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