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The Gymnast

A gymnast receives the following scores from five different judges at a state competition:

 Event Judge 1 Judge 2 Judge 3 Judge 4 Judge 5 Floor a 9.3 8.1 8.9 9.5 Bars 7.6 8.2 8.5 8.2 8.9 Vault 9.5 8.9 9.4 a a Beam 8.4 8.5 8.4 a 8.7

The "a" represents an unknown value. It can be any value from 0.0 to 10.0, but "a" must be the same in all four events.

To find her score for each event, the highest and lowest scores in that event are thrown out. Then the average (mean) of the remaining three scores is computed.

Open the file gymnast.xls. Use this spreadsheet to help you answer the following questions. I have made it so that the columns will be summed for you, and I have entered a "starting" formula to calculate the mean for each column. I have used 1 for the denominator. You will need to change this. You can do this by clicking on the formula bar at the top and changing 1 to whatever value you need.

1. What are some advantages and disadvantages to this type of scoring?

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2. What are all possible values of "a" if the vault was her worst event? Tell how you find your answer and explain why it works.

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3. What are all possible values for "a" if the vault is her best event? ? Tell how you find your answer and explain why it works.

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Which of the events do you think is her best event? Why do you think so? Does your answer depend on the value of a? Why or why not?

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By now, many of you are probably thinking that you wishyour own math teacher would compute your average in this same way. Let's see what would happen if you had 5 test grades and I were to drop the lowest and highest grade before computing the mean.

Using the spreadsheet, try this out using several different scores for the five tests. Make a chart comparing what the mean would be with all five scores to what it would be after dropping the highest/lowest. Using this information, which way do you wish your math test averages were computed? Be sure to include your chart and reasons for your decisions below?