Question

mr. malloy wants to make sure amo and javier get the best possible grade after five tests and can either give a grade based on the median or the mean.

test1
number\t1\t2\t3\t4\t5
amos scores\t97\t92\t89\t55\t90
javiers scores\t68\t97\t65\t92\t65

what measure of center should mr. malloy use for amo and for javier for the best possible grade?

○ the teacher should use the mean for both amo and javier.
○ the teacher should use the median for both amo and javier.
○ the teacher should use the median for amo and the mean for javier.
○ the teacher should use the mean for amo and the median for javier.

Explanation:

Step1: Calculate Amo's mean and median

• Mean:

$$\text{Mean}=\frac{97 + 92+89 + 55+90}{5}=\frac{423}{5} = 84.6$$

• Median:

Sort the scores: \(55,89,90,92,97\). The median is the middle - value, which is \(90\).

Step2: Calculate Javier's mean and median

• Mean:

$$\text{Mean}=\frac{68+97 + 65+92+65}{5}=\frac{387}{5}=77.4$$

• Median:

Sort the scores: \(65,65,68,92,97\). The median is the middle - value, which is \(68\).

Since Amo has an out - lier (\(55\)) which pulls the mean down. The median is less affected by outliers. For Amo, the median (\(90\)) is higher than the mean (\(84.6\)). For Javier, the mean (\(77.4\)) and median (\(68\)): the mean is higher. But if we want to give the best possible grade, for Amo, using the median gives a better score. For Javier, using the mean gives a better score. But if we consider the nature of measures (median for skewed data (Amo has a low out - lier), mean for relatively symmetric data (Javier's data is more symmetric around a certain value when considering non - outlier behavior in a simple sense as there is no extreme out - lier like Amo's \(55\))). But actually, if we calculate accurately:
Another way:
For Amo:
Sort scores: \(55,89,90,92,97\)
Mean \(=84.6\), median \(=90\)
For Javier:
Sort scores: \(65,65,68,92,97\)
Mean \(=\frac{65 + 65+68+92+97}{5}=\frac{387}{5} = 77.4\), median \(=68\)
Since Mr. Malloy wants to make sure they get the best possible grade. For Amo, the median (\(90\)) is better than the mean (\(84.6\)). For Javier, the mean (\(77.4\)) is better than the median (\(68\))

Answer:

The teacher should use the median for Amo and the mean for Javier.