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?
Answers
Mr. Malloy should use the mean for both Amo and Javier.
Given:
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 1 2 3 4 5
Amo’s Scores 97 89 55 55 90
Javier’s Scores 68 65 92 92 65
To find:
What measure of center should Mr. Malloy use for Amo and for Javier for the best possible grade?
Solution:
To determine the best measure of center for Amo and Javier's grades, calculate the median and mean for each student.
For Amo:
Median:
To find the median arrange the score in ascending order
Amo's scores are in ascending order: 55, 89, 90, 92, and 97.
The middle score is 90, so the median is 90.
Mean:
To find the mean, add up all of Amo's scores and divide by the number of tests:
= (97+92+89+55+90)/5 = 84.6.
For Javier:
Median:
To find the median, arrange the score in ascending order
Javier's scores are in ascending order: 65, 65, 68, 92, and 97.
The middle score is 68, so the median is 68.
Mean:
To find the mean, add up all of Javier's scores and divide by the number of tests:
=> Mean= (68+97+65+92+65)/5 = 77.4.
The teacher should use the mean for both Amo and Javier for the best possible grade. The mean gives an average score, which takes into account all the scores and can provide a more accurate representation of their overall performance.
Hence,
Mr. Malloy should use the mean for both Amo and Javier.
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the mean may be an appropriate measure of center for both students. Mr. Malloy should use the mean to determine the best possible grade for Amo and Javier after the five tests.
To determine the best measure of center for Amo and Javier's grades, we need to consider their scores on the five tests. Mr. Malloy can either use the median or the mean as the measure of center.
If Mr. Malloy chooses to use the median, he will find the middle value of each student's scores when they are arranged in ascending order. For Amo, the median score is 90, while for Javier, the median score is 68.
If Mr. Malloy chooses to use the mean, he will add up each student's scores and divide the total by the number of scores. For Amo, the mean score is 84.6, while for Javier, the mean score is 77.4.
Which measure of center is best depends on the nature of the data. If the data is skewed or has outliers, the median may be a better measure of center.
However, if the data is normally distributed and does not have outliers, the mean may be a more appropriate measure.
In this case, both Amo and Javier have scores that are relatively close to each other, and there are no clear outliers.
Therefore, the mean may be an appropriate measure of center for both students. Mr. Malloy should use the mean to determine the best possible grade for Amo and Javier after the five tests.
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