I'm looking for some statistics on typical Harry Potter chapter word count.
A nicely graphed distribution would be nice, but I'll accept an answer that has something equivalent to the average, standard deviation, and quartiles.
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To calculate this answer I used the text from the official Pottermore ePubs (each chapter is saved as a seperate html file). I ran the htmls through a utility I found to convert them to txt, and then used the unix
wc -w command to generate a list of chapter word counts. (Feel free to play around with the data on your own.)
I plugged this into excel and did a few calculations.
Note: All the below data uses the UK text. The American text tends to be a bit shorter.
Here is how the distribution looks with a bin width of 500 words.
However it's worth noting that some factors have a significant effect on chapter length, such as the length of the book and the position in the book.
For the series as a whole, we can tabulate the number of chapters and length of the books, and find the weighted average of the length of a chapter (read this to see what a weighted average is and why you can't just take an "average of averages").
So the weighted average chapter length across the whole series is 5542 words (rounded to the nearest whole word). If I had a source to determine the word length per chapter of each book, we could find a weighted average per book and then take a weighted average of that, but I don't imagine that'd stray too far from the 5542 calculated here.
Standard deviation is a little trickier, as with all of the different books to consider a weighted standard deviation would be more appropriate. After much toiling in Excel with the equation, I finally got a result of 747 (rounded to the nearest whole word, 746.5898815 exactly).
With these values, we can get a lovely normal distribution.
Using the weighted mean and weighted standard deviation, the chapter length can be normally distributed (see link at bottom to do this yourself). In this image, we can see that the probability of a chapter having more than 6000 words is about 27%.
Not sure how useful they'll be for you, but anyway the quartiles are as follows (nearest whole word):
Q1 = 5038
Q2 = 5542
Q3 = 6045