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.
2026-03-25 11:15:53.1774437353
Average of a dataset with Ranges of Numbers - A "Simple" high school standarized test question
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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.