Distances to brightest naked eye stars

I saw this recent xkcd comic, and had to figure out how many of the naked eye stars are more than 1000 light-years away.

It took me awhile to find a star catalog that was easy to search which also had both the apparent magnitudes and the distances to the stars, but I was able to locate a database of over 87,000 stars in CSV format.

First I found all the stars with magnitude 6.0 or brighter. That narrowed the list down to just over 5,000 stars. Putting the distances into plot.ly, I created this histogram:


Each bar represents a bin of width 100 parsecs. My interest in stars 1000 light-years means I have to look at the stars more than 300 parsecs away. I added up the stars in the first three bins, which represented about 87% of all the visible stars.  So my estimate of the naked eye stars which are 1000 light-years away or more is about 13%.

So, assuming on a clear night (no moon, ideal viewing conditions) I could see somewhere between 2000-3000 stars total, only about 250-400 stars would be more than 1000 light years away.

Of course, looking through a telescope changes that figure completely.