I hate to be the bearer of bad news for some, but YES, there IS an average number of showings to sell a house. It may vary across regions or across time, but at any given point in time, and for any given region, there absolutely IS a statistical average.
I apologize that I do not know the specific answer, but I feel badly for Chad asking a question, then receiving over half of the responses saying there is no average, when there absolutely is such a number. A real estate professional may not know what the average is, but that does not mean that the average does not exist. The fact that the sample set may vary greatly from the average also does not limit the fact or authenticity of the average.
How any specific property will sell in relation to number of showings will certainly vary from that average, in high relation to condition, the market, the price, and the preparation. But, variances are expected ... without variances there would be no meaning to a statistical average.
As with any sampling of occurrences, there is an average, a mean, a standard deviation, and a variance. They are all strictly defined as a means of describing a set of varying occurrences.
Good luck Chad.