# Statistics for the final

### Overall distribution of scores

This is a smooth histogram of raw exam scores. The area under an interval closely approximates the number of exams scoring in that interval. The larger the interval, the more accurate the approximation.

### Scores per problem

The explanation of the “box and whiskers” plot is as follows: The top line reaches from the maximum grade down to the first quartile (that is, the top fourth of the class received grades in that range). The box shows the range from the first quartile down to the third; the middle half of the class got those grades. The bottom line stretches down to the minimum grade. The horizontal tick marks show the median, dividing the upper half from the lower half of the class. Finally, the central dot shows the mean, or average, grade on the problem.

I don't include zeroes in any of these statistics.