Find the average of first seven prime numbers.

Question

Accepted Answer

To find the average of the first seven prime numbers, we first need to identify these prime numbers and then calculate their average.

The first seven prime numbers are: 2, 3, 5, 7, 11, 13, and 17.

1. **Calculate the sum of these prime numbers:**

$$
   2 + 3 + 5 + 7 + 11 + 13 + 17 = 58
   $$

2. **Calculate the average:**

The average is calculated by dividing the sum of the numbers by the number of numbers.

$$
   \text{Average} = \frac{\text{Sum of the numbers}}{\text{Number of numbers}} = \frac{58}{7}
   $$

3. **Perform the division:**

$$
   \frac{58}{7} = 8 \frac{2}{7}
   $$

Therefore, the average of the first seven prime numbers is $8 \frac{2}{7}$, which corresponds to Option 4.

**Explanation of why other options are incorrect:**

- **Option 1 (8):** This option suggests that the average is 8. However, as calculated, the exact division of 58 by 7 results in $8 \frac{2}{7}$, not 8. Therefore, Option 1 is incorrect.

- **Option 2 (9):** This option suggests that the average is 9. Since $8 \frac{2}{7}$ is less than 9, Option 2 is incorrect.

- **Option 3 ($8 \frac{1}{7}$):** This option suggests that the average is $8 \frac{1}{7}$. However, the correct calculation gives $8 \frac{2}{7}$, making Option 3 incorrect.

In conclusion, the correct answer is Option 4, $8 \frac{2}{7}$, as it accurately represents the average of the first seven prime numbers.