Question

peters teacher says he may have his report card percentage based on either the mean or the median and he can drop one test score if he chooses. 84%, 71%, 64%, 90%, 75%, 44%, 98% which measure of center should peter choose so he can have the highest percentage possible? peter should choose the mean after dropping one test score. peter should choose the mean without dropping one test score. peter should choose the median after dropping one test score. peter should choose the median without dropping one test score.

Explanation:

Step1: Sort the data

Sort the test scores: \(44\%,64\%,71\%,75\%,84\%,90\%,98\%\)

Step2: Calculate the median without dropping

For \(n = 7\) (odd number of data points), the median is the \(\frac{n + 1}{2}\)th value. \(\frac{7+1}{2}=4\)th value. The median is \(75\%\)

Step3: Calculate the median after dropping the lowest score (\(44\%\))

New data set: \(64\%,71\%,75\%,84\%,90\%,98\%\). For \(n = 6\) (even number of data points), the median is \(\frac{3\text{rd}+4\text{th}}{2}=\frac{75\% + 84\%}{2}=79.5\%\)

Step4: Calculate the mean without dropping

Mean\(=\frac{44 + 64+71+75+84+90+98}{7}=\frac{526}{7}\approx75.14\%\)

Step5: Calculate the mean after dropping the lowest score (\(44\%\))

Mean\(=\frac{64 + 71+75+84+90+98}{6}=\frac{482}{6}\approx80.33\%\)

Answer:

Peter should choose the mean after dropping one test score.