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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.

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