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Mean or Median?

Three students, Jawahn, Lisa and Herbie, are studying for the last of five history tests in the current marking period. In math class they have learned how to calculate the mean and median of a set. Their first four history test scores are listed (twice) in a table below.

Student         Fifth test Mean score Median score
Jawahn 96 100 89 95      
Jawahn 96 100 89 95      
Lisa 75 82 100 77      
Lisa 75 82 100 77      
Herbie 86 40 79 89      
Herbie 86 40 79 89      

Let’s say that you are the teacher. You must decide whether to use the mean or the median of the five test scores to assign a History grade to all students. You will announce your decision before the fifth test is given.

1. Invent two possible scores that each student might earn on the fifth test, and calculate the means and the medians for those six sets of scores.

2. Make a bar graph showing a comparison of the mean and median for all six sets. This can be achieved by using one color bar for the means, side by side with another color for the medians. Your graph might look like the one below. Be sure to give it a title, a key (or legend) and label the scales.

3. Using complete sentences, write three observations about the results you find. Give your decision (as the teacher) whether you will use the mean or the median to determine the history grade for all students, and give two reasons to support your decision.

Solution

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