Can I create statistics for each assignment?
For quizzes, there are quiz statistics: Once I publish a quiz, what kinds of quiz statistics are available?
For graded assignments, not just quizzes, you can go to the Gradebook and select "Assignment Details" from the drop down menu at the top of any column.
The statistics are limited to a box plot, mean, minimum, maximum, and sample size. Another concern of people is that if someone gets a zero for any reason, including not completing the assignment, that shows up as the low score and is computed into the average.
If someone wants more than that, you can export the gradebook and bring it into some software to analyze it: How do I export grades from the Gradebook?
Note: All of those links are for the legacy gradebook, which is being phased out, but hopefully the new gradebook is close enough that you can find things.
To add to the information James provided, some of this information is in the new gradebook, but the assignment detail information has been moved to Analytics 2.0.
In the new gradebook you can look at "Individual View" - How do I use the New Gradebook? (it's under Grades --> Gradebook pull down --> Individual View --> Content View --> Select assignment) - to see points possible, average, high, and low score. Below is an example of how this looks.
**Note, this view shows this information as a "score," which means points on the assignment.
In Analytics 2.0 (What is Analytics Beta?), you can click on any of the data points on the chart (or table) to see average, high, low, and a table showing grade breakdown (if you mouse over a column you'll get the exact number of students in that column and the percent range the column represents). Below is how this looks when you click on a data point.
**Note, this view shows this information as a "percentage" and does not show point value.
Retrieving data ...