Where in the world are those 18.6 million iPod touches?

Apple (AAPL), for reasons known only to itself, does not report the number of iPod touches it has sold.

But it lets you do the math, and on Tuesday COO Tim Cook casually mentioned, in response to a question about the App Store, that the total installed base of iPhones (26.4 million) plus iPod touches (X) is now 45 million.

So where are those 18.6 million iPod touches?

Nearly 12 million are in the United States, according to a report on the geographical distribution of Apple mobile devices issued Thursday morning by AdMob, the leading mobile ad platform. That makes sense, given that Americans buy the lion's share of all Apple handsets, and the company has been particularly aggressive about marketing the iPod touch to U.S. students in its back-to-school computer sales.

But if you look at AdMob's region-by-region breakdown, the iPod touch is surprisingly popular overseas.

In Latin America, for example, the ratio of iPhones to iPod touches is virtually identical to North America's. Apple has sold more than 327,000 in Mexico alone, according to AdMob's estimates, which apparently is more than the total number of iPhones sold in that country.

iPod touches are even more popular in Canada. According to AdMob, Canadians have purchased more than 1.36 million iPod touches but only 805,594 iPhones.

iPod touch sales are also strong, relative to iPhone sales, in Oceania, Asia and Western Europe. The device is less popular in Africa and least popular in Eastern Europe.

Wordwide, according to AdMob, the ratio of iPhones to iPod touches on its network in June was roughly 2 to 1. In other words, iPhones represented 68% of Apple handsets and the iPod touch made up the other 32%. This ratio has remained constant over the last several months, according to AdMob, implying a similar growth rate for both devices worldwide.

Below: AdMob's country-by-country iPod touch sales estimates, obtained by multiplying AdMob user shares in each country by the total number of iPod touches sold.

Here's the comparable chart for iPhones.

AdMob describes itself as the world's largest mobile advertising platform, serving banner and text link ads on mobile web pages for more than 7,000 publishers. It collects handset and operator data on each of the nearly 95 billion ads it has served since 2006, which enables it to produce charts like these.

For a pdf of the full report, click here.