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== Distribution == ## page was renamed from Final exam
<<lia(final_hist.png, width=50%, align=right)>>
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<<lia(final_hist.png, width=50%, align=right)>>
Here is the histogram of the final exam scores. If you have a good imagination, then you can imagine a bell shape. More realistically, though, the distribution is skewed left, while it also features a long fat tail at right.
== Score distribution ==

Here is the histogram of the final exam scores. If you have good imagination, then you can perhaps see a bell shape...with a fat long tail at high score end.

== Curving ==

You might have noticed that some students got more than 100 points according to the above histogram. How is this possible? First of all, note that the total score of the exam was 105, instead of 100. So, 5 points were extra credit points. Second, after grading was completed, I curved the scores just as I did for the midterm. That is, I took the average performance of students for problems 1&ndash;5, and then uniformly increased all scores for problems 6 through 9 so that the average percentage scores for these later problems matched the average percentage score for problems 1&ndash;5.

For your information, before the curving, the average score was 52.6. After the curving it was 66.8.

Inlined image: final_hist.png

Score distribution

Here is the histogram of the final exam scores. If you have good imagination, then you can perhaps see a bell shape...with a fat long tail at high score end.

Curving

You might have noticed that some students got more than 100 points according to the above histogram. How is this possible? First of all, note that the total score of the exam was 105, instead of 100. So, 5 points were extra credit points. Second, after grading was completed, I curved the scores just as I did for the midterm. That is, I took the average performance of students for problems 1–5, and then uniformly increased all scores for problems 6 through 9 so that the average percentage scores for these later problems matched the average percentage score for problems 1–5.

For your information, before the curving, the average score was 52.6. After the curving it was 66.8.