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This is similar to a question on a standardized test for high school students: The heights of students are listed below. What is the mean of this dataset? The dataset is: 1 student 55-56 inches, 1 student 57-58 inches. The first thing that confuses me is that 55-56 and 57-58 are not adjacent meaning that the numbers between 56 and 57 are not part of the dataset? Or is the "-" symbol inclusive meaning 55-56 includes 56.5? This doesn't seem mathematically correct because inclusive means that the point of the upper bound would be included, not a whole inch. Or were the heights of students measured to the nearest inch? Also what is the average of ranges? Would the answer be 56-57? Or 56.5? This is further complicated by the confusing ranges that I mentioned above. I find it absurd that the standardized test would contain a question that does not have a standardized answer. Often I get perfect scores on standardized tests but I probably got this one wrong. If anyone could explain the reasoning behind the right answer it would clear things up for me.

dan dan
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    There is more than one possible answer here. Even if we give you what we perceive as the right answer, it will do little to sway the grader of your test. I advise you to seek out somebody who has experience grading such tests. There cannot be any harm in asking them. – Carl Christian Jun 02 '18 at 19:01

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If all the height ranges had a gap like this then the interpretation that makes most sense is the height range $55 - 56$ inches is in fact $54.5$ to $<56.5$, and $57 - 58$ is $56.5$ to $<58.5$ etc. It is continuous data made somewhat discrete to simplify the calculation.

If it didn't, that is, some taller ranges went from $60 - 61, 61 - 62$ etc., then the interpretation would be that there was no student in the $56 - 57$ range. Either way, to calculate the overall mean would mean taking the middle value which would be $55.5$ for the $55 - 56$ range

Also, a question that leaves the student guessing the correct interpretation is a somewhat poorly conceived question.

Phil H
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