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 t
he 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.
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.
2 answers:
The data has been properly arranged in tabular form and is shown below in the image.
First we need to find the mean and median of scores of both students.
1) For Amo:
Mean =
Median = Middle Value when data is arranged in ascending order = 90
2) For Javier:
Mean =
Median = Middle Value when data is arranged in ascending order = 92
For both the students, value of Median is larger then the mean. So in order to give the best possible grade Mr. Malloy should use the median score for both students.
First we need to find the mean and median of scores of both students.
1) For Amo:
Mean =
Median = Middle Value when data is arranged in ascending order = 90
2) For Javier:
Mean =
Median = Middle Value when data is arranged in ascending order = 92
For both the students, value of Median is larger then the mean. So in order to give the best possible grade Mr. Malloy should use the median score for both students.
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Answer:
Where and
And the z score is given by:
And since z = 0.75 we can replace like this:
And if we solve for x we got:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the ACT scores of a population, and for this case we know the distribution for X is given by:
Where and
And the z score is given by:
And since z = 0.75 we can replace like this:
And if we solve for x we got: