Now, you will consider Option 1, setting a maximum shower time of 10 minutes.
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Assume all students who showered longer than 10 minutes will now shower for
exactly 10 minutes. Assume the rest of the students will shower for the same amount
of time as they did yesterday.
Blake claims Option 1 would result in the class mean going below 8 minutes, but the
class median would not change.
Explain whether you agree or disagree with Blake's claim. Include the class mean and
median that would result from Option 1 in your explanation.
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MrRoyal MrRoyal · Answer 1 · 2022-05-14T09:25:17+02:00

The maximum shower time is an illustration of mean and median, and the conclusion is to disagree with Blake's claim

The question is incomplete, as the dataset (and the data elements) are not given.

So, I will answer this question using the following (assumed) dataset:

Shower time (in minutes): 6, 7, 7, 8, 8, 9, 9, 9, 12, 12, 12, 13, 15,

Calculate the mean:

Mean = Sum/Count

So, we have:

Mean = (6+ 7+ 7+ 8+ 8+ 9+ 9+ 9+ 12+ 12+ 12+ 13+ 15)/13

Mean = 9.8

The median is the middle element.

So, we have:

Median = 9

From the question, we have the following assumptions:

The shower time of students whose shower times are above 10 minutes, is 10 minutes
Other shower time remains unchanged.

So, the dataset becomes: 6, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 10, 10

The mean is:

Mean = (6+ 7+ 7+ 8+ 8+ 9+ 9+ 9+ 10+ 10+ 10+ 10+ 10)/13

Mean = 8.7

The median is the middle element.

So, we have:

Median = 9

From the above computation, we have the following table:

Initial Final

Mean 9.8 8.7

Median 9 9

Notice that the mean value changed, but it did not go below 8 as claimed by Blake; while the median remains unchanged.

Hence, the conclusion is to disagree with Blake's claim