In order to fill out the mean-frequency table and calculate the average price of a product sold by the factory last month, we need the following steps:

1. Identify the price ranges for each product category: We need the price ranges for classic, regular, and premium products, which is normally provided in the table.
2. Assign a mid-point price to each range: The mid-point price (also called the class mark) represents the average price in each range. If the price ranges are given, the mid-point is the average of the lower and upper bounds of each range. This value will be used for further calculations.
3. Create a frequency table: For each product type (classic, regular, and premium), use the corresponding frequency of sales (37 for classic, 104 for regular, and 42 for premium).
4. Calculate the total sales for each product type: Multiply the mid-point of each price range by the frequency of sales for that category.
5. Calculate the overall average price: The average price is given by the formula:

$\text{Average Price} = \frac{\sum (\text{Mid-point Price} \times \text{Frequency})}{\text{Total Number of Products Sold}}$

Let's break this down step by step. Could you provide the price ranges for the classic, regular, and premium products? With that information, we can proceed to complete the table and find the average price.

Would you like to proceed with this?