How can I use only the most recent data in an average?

I have a class which has regular listening quizzes. If a student's average from the last three tests falls below 10 points (out of 20), then that student has to come in for extra practice.
My Sheets are set up with the students' names running down column A. Test 1 is column B. A a check box for whether students handed in the pre-listening homework is in column C. The test and homework column pattern is continued for tests 1 through 20.
I then have an average for all the tests for that student further over to the right.
Next to the overall average, I would like to make a column with an average showing only the latest three test scores. So, for example, the students have just finished test 10, the average of test 10, 9 and 8 would appear, but everything prior to that would be ignored.
I appreciate any suggestions on a formula for how I could make that happen.
Thank you!

CB,
Here's one approach. Note that I used Header Columns to make the programming easier. If you choose not to use Header Columns, you can adjust the formulas to account for the difference.
The formula in Overall Average is: =IFERROR(AVERAGE(2:2), 0) for Alice. Fill Down.
The formula in Last Three Scores average is: =IF(COUNT(2:2)<3, B, AVERAGE(OFFSET(D2, 0, (COUNT(2:2)-3)*2, 1, 6))) for Alice. Fill Down.
Regards,
Jerry

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