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.

Test
Number
Amo’s Scores
Javier’s Scores
1
97
68
2
92
97
3
89
65
4
55
92
5
90
65

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.

Answer 1

To determine whether Mr. Malloy should use the mean or the median for Amo and Javier, we will calculate both the mean and the median of their scores.

### Amo's Scores:
- Scores: 97, 92, 89, 55, 90

**Mean Calculation:**
\[
\text{Mean} = \frac{97 + 92 + 89 + 55 + 90}{5} = \frac{423}{5} = 84.6
\]

**Median Calculation:**
To find the median, we first sort the scores:
- Sorted Scores: 55, 89, 90, 92, 97
- The median (middle value) is 90 (3rd value in sorted list).

### Javier's Scores:
- Scores: 68, 97, 65, 92, 65

**Mean Calculation:**
\[
\text{Mean} = \frac{68 + 97 + 65 + 92 + 65}{5} = \frac{387}{5} = 77.4
\]

**Median Calculation:**
To find the median, we first sort the scores:
- Sorted Scores: 65, 65, 68, 92, 97
- The median (middle value) is 68 (3rd value in sorted list).

### Summary of Results:
- Amo: Mean = 84.6, Median = 90
- Javier: Mean = 77.4, Median = 68

### Conclusion:
- **For Amo**: The median (90) is higher than the mean (84.6), so Mr. Malloy should use the median.
- **For Javier**: The median (68) is higher than the mean (77.4), so Mr. Malloy should use the mean.

### Final Decision:
The teacher should use the median for Amo and the mean for Javier. Thus, the correct answer is:

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