SOLUTION: Sam made the following scores on unit tests for the term: 92, 98, 15, 92, 87, 92 Sam's teacher said that his grade would be based on the mean of his grades. Sam argued that his g

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Question 783669: Sam made the following scores on unit tests for the term:
92, 98, 15, 92, 87, 92
Sam's teacher said that his grade would be based on the mean of his grades. Sam argued that his grade should be based on the median score of his grades. Find the mean and the median of Sam's grades. Which do you think best reflects Sam's work for the term? Explain your answer

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
92, 98, 15, 92, 87, 92
The median is the middle value, so I'll have to rewrite the list in order:
15, 87, 92, 92 , 92, 98
There are six numbers in the list, so the middle one will be the %286+%2B+1%29%2F+2+=+7+%2F+2+=+3.5th number:
which is 92
The mean is the usual average:
%2815%2B87%2B92%2B92+%2B92%2B98%29%2F6=79.33
teacher said that his grade would be based on the mean, and we know that
medians are less sensitive to extreme+scores and are probably a better+indicator generally of where the middle of the class is achieving, especially for smaller+sample sizes like here
means are the arithmetic+average and are often used with larger+sample sizes;
so, Sam argued that his grade should be based on the median score of his grades and he is right because +sample size is smal and 92 is a better+indicator of his grade