Was the math/statistics application in this article correct? I don't know high level math or statistics and wanted to ask about the math in a recent online article. The website 'TheMarySue.com' has an article saying:

ON AVERAGE, THE TOP WOMEN-LED FILMS OF 2013 GROSSED HIGHER THAN MALE-LED FILMS

and then references this article that did the math:
"Women-Centric Films Out-Gross Male-Centric Films on Average: Twist!"
In that article the way the author determined that "Actress-centered movies out-grossed actor-centered movies by almost exactly one-third!" was by using the following:

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*Total gross of all the top 100 movies in 2013: \$10.039 billion.

*Total gross of 15 actress-centered movies: \$1.908 billion.

*Total gross of 79 actor-centered movies: \$7.525 billion.

*Average gross of actress-centered movie: \$127 million.

*Average gross of actor-centered movie: \$95 million.

The author says 15 movies of 2013 had a female lead in his view, 5 were 'neuter' and 79 had a male lead.
I am not trained in statistics but it seemed to me that the author didn't apply math correctly. For example, I used his same logic to show that movies with numbers in the title grossed more than title without numbers:

*

*Total gross of all the top 100 movies in 2013: \$10.048 billion.

*Total gross of 18 number-included-titled movies: \$2.110 billion.

*Total gross of 82 letters-only movies: \$7.938 billion.

*Average gross of number-included-titled movies: \$117 million.

*Average gross of letters-only movies: \$96 million.

I would think that does not show that movies with titles that had numbers were correlated to higher-returns, but a lot of people are telling me that I am wrong and that the argument made in the article based on the data is "sound" and "solid." One person on the comments section of TheMarySue says:

Yeah, I was really happy about the article until I got to their statistics and realized the logic was flawed. :(
More films on the lower end of the spectrum means the average gets pulled lower.

So I am confused because everyone else says the logic and the applied statistics is sound. :(
I don't have a preference of gender lead roles in movies. I thought the division of gross revenue to argue that those movies had some special quality was incorrect. I am trying to answer the question:
"What affect does a male lead or female lead have in the gross revenue of a movie in top 100 films of 2013?"
by limiting myself to that writer's data.
How I am wrong in the application of division to create a sound argument for their premise so I don't make that mistake again? Also, what kind of math or techniques should be used to answer that question?
Thanks!
 A: First off, the article's statistic is a very misleading statistic, and I would even say useless. By using the proportion of the top 100 movies, the movies only represent a small (not random) sample of all movies in the year. Only 15 women were in the top 100 and 79 males.  Based on this fact that there are more Male-centric movies in the top 100, one could argue male-centric movies were better as a whole; but that would also be misleading. What proportion of all lead roles are cast with males or females? For the sake of argument, suppose only 15 movies all year are cast with female lead, then females sure are looking good (all 15 got into the top 100!!!). Now, suppose an equal number of movies starred male and female leads for the year.  Now females are looking pretty bad (only 15 in the top 100???). You get the picture.  By only looking at the top of the distribution of movie grossings, you are ignoring much of the information necessary to make any useful conclusions.
Furthermore, it is very likely that that these movie grossings are skewed to the right, so median would be a better measure of center for comparison, if a correct comparison was made in the first place.  A single highly paid female (outlier) could account for the difference in pay.  
If you want a somewhat valid measure of relative success, you would need a sample that represents all movies, or at the very least, an idea of how many male/female movies there are overall.  Even then, you have other confounding variables (e.g. what if one gender's movies tend to be lower budget?).
