Analysis of sells (what to buy)

Question

Statistical analysis is not my field, so forgive me if this is a very stupid question.

I have a list of sold items by size. Shoes in this case

Size    Qty
35  2
36  1
37  4
38  4
39  32
40  17
41  23
42  57
43  95
44  90
45  98
46  33
47  16
48  4
total:  476

I have to tell the owner how much of every size to buy. The problem is, I can't say him. - You should buy 95 shoes size 43 for every one of size 36...

The usual practice is to buy the whole size curve and buy extras for the most selling sizes.
This is about a year worth of data. How should I present this information in an easy to understand way? What I want to present is a general rule. Something like "for every size curve, you should buy x additional shoes of size x".
The idea would be to later apply this approach to other clothing items.

Answer 1

Following on from Rob's answer, you could estimate an acceptable level using a Normal approximation. So if an acceptable rate of running out is 5%, then use the following rule:

Qty + 1.644 * Qty^(0.5)

The value 1.644 comes from the Normal or Gaussian distribution.

Other acceptable rates could be:

1. 1%: change 1.644 to 2.326
2. 10%: change 1.644 to 1.282

Further Rationale

Rob suggested that you could model your data using a Poisson distribution. When the rate (or in your case Qty) is large (say 10), then the Normal distribution gives a good approximation. The following graph shows the Poisson 95th percentile (red) and the Normal approximation in green. As you can see they are fairly close. The raw data is shown as points.

Answer 2

I suggest he stocks $y_s$ pairs of shoes of size $s$ where $y_s$ is chosen so that the probability of running out of stock before the next delivery is set to some acceptable level (e.g., 5%).

It seems reasonable to assume $y_s$ is Poisson with rate $\lambda_s$. You can estimate $\lambda_s$ as the average sales of that size over the last few delivery periods. Then all that remains is to find the 95th percentile of the Poisson distribution with mean equal to the estimated rate for each size.