Using a free AI program I input your exact statement and received this:

To calculate a running average (also known as a cumulative average) as you go along a column of numbers, you can use the following formula:

If \( S_n \) is the sum of the first \( n \) numbers, and \( n \) is the count of those numbers, the running average \( A_n \) can be calculated as:

\[
A_n = \frac{S_n}{n}
\]

Where:
- \( A_n \) is the running average after \( n \) numbers.
- \( S_n \) is the running sum of the first \( n \) numbers.
- \( n \) is the total count of numbers you have processed so far.

### Steps to Calculate the Running Average:

1. **Initialize Variables**:
   - Start with a `running_sum` set to 0.
   - Start with a `count` set to 0.

2. **Iterate Through Each Number**:
   For each new number \( x_i \) in your column:
   - Update the `running_sum`:
     \[
     \text{running_sum} = \text{running_sum} + x_i
     \]
   - Update the `count`:
     \[
     \text{count} = \text{count} + 1
     \]
   - Calculate the running average:
     \[
     A_n = \frac{\text{running_sum}}{\text{count}}
     \]

3. **Store or Output the Average**:
   You can store or print the average after each iteration if needed.

### Example:
Let's say you have the numbers 4, 8, and 10.

1. Start with `running_sum = 0` and `count = 0`.
2. After adding 4:
   - `running_sum = 0 + 4 = 4`
   - `count = 0 + 1 = 1`
   - \( A_1 = \frac{4}{1} = 4 \)
3. After adding 8:
   - `running_sum = 4 + 8 = 12`
   - `count = 1 + 1 = 2`
   - \( A_2 = \frac{12}{2} = 6 \)
4. After adding 10:
   - `running_sum = 12 + 10 = 22`
   - `count = 2 + 1 = 3`
   - \( A_3 = \frac{22}{3} \approx 7.33 \)

With this method, you will maintain a running average as you add new numbers to your column!