# Math 12

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The mean and standard deviation of a set of data are two measurments that describe the data. A certain student has written 8 out of 10 unit exams, which are equally weighted. The student misses the ninth exam and receives a score of 0. However, for the last exam, the student studied and scored a 100%. Compare the mean and standard deviation after 8 unit tests and after 10 unit tests. My question is how do I find the mean and standard deviation when all I know is the mark on the 9th test is 0 and the tenth 100%. How do I do this question when I don't know any other marks. Please help I've never had a question with such limited information. I was told it really is possible to solve it with the information given.

• Math 12 -

The mean % score after 8 exams is M, and the sum of the scores is 8 M. After 10 exams the sum of scores is 8M + 100 and the new mean is (8M +100)/10 = 0.8M + 10. Compare that with M. It is lower by (0.2M -10)

A similar approach can be used for the new standard deviation. The answer will depend upon the previous 8-test standard deviation and mean.

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