算法找到最畅销的价格

Question

I have sales data from some our online listings. I randomly priced the same item to find the optimum price in an attempt to yield the most profit. Below is some of our sample data:

6 units @ 296.9/ea 
225 units @ 331.69/ea 
45 units @ 334.99/ea 
5 units @ 369.29/ea 
2 units @ 399.0/ea 
2 units @ 353.27/ea 
5 units @ 354.21/ea

It's pretty obvious which is the best price range, however I'm still trying to find some sort of average so we don't just pick the highest numbers.

My original thought was to simply multiply each set, add them all up, and divide by the total units (aka, finding the total average). The problem with that there is no consideration for the relationship between the amount of units sold and the price for each.

Does anyone have any advice for a way to find the best solution? Thanks!

--EDIT--

Factoring in analytical data such as click and view rates shouldn't be needed since all listing were done at the exact same time and were all the exact same. The amount of sales, views, etc are a direct result of the pricing. In other words, we are getting the sales based on what we price the item.

I'm not trying to find any profit margins, I'm trying to find the best LIST PRICE. We are already checking our profit margins and enabling/disabling campaigns thar are not meeting our thresholds. We're trying to find a medium price based on previous results so we can go into new markets and have an idea at an ideal price.

--2nd Edit--

When we list identical items for testing, regardless of price, some do get more views overall which does in fact result in more sales. Almost as if they go "viral" on the store. The reason for those views are completely out of our control. Every listing is identical except for pricing. Almost all online retailers have special algorithms to fetch the best match result to that customer.

The only reason we're trying to do this is to try and get an educated "guess" on the optimal list price based on previous results, regardless of how we obtained them. In other words, the stores and the customers are picking these prices for us, we just want to try and guess the price to start from instead of pricing listings randomly. From there we can work on increasing our margins.

Answer 1

This is more of a methodological critique (comment), but it's too long for the comments field and it is sort of and answer. But the basic answer to your question is that it is unanswerable given the data that you're providing:

1. How many times were each of these values presented to customers? It's a little surprising that you only sold 6 units at the lowest price... this leads me to believe that customers were not exposed equally to each of these price levels. You need to get the conversion rate delivered by a price level by calculating: number_of_times_this_price_was_shown divided by the number_of_times_customer_bought_item_at_this_price

2. What is your profit margin on each item? Selling 100 widgets at $5.01/widget is better than selling 5 widgets at $10.00/widget if my widgets cost me 1cent/widget, but if they cost me $5.00/widget then it's better to sell only 5 widgets at $10.00/widget ($5.00 profit/widget * 5 widgets = $25.00, vs one cent profit/widget * 100 widgets = $1.00).

If you can tell us those two pieces of information we can provide the correct algorithm.