Question

Determine whether the following statement makes sense or does not make​ sense, and explain the reasoning.
The mean can be misleading if you​ don't know the spread of data items.
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Part 1
Choose the correct answer below.
A.
The statement does not make sense because the mean measures the spread of the data items.
B.
The statement makes sense because mean is not always the true average of the data.
C.
The statement makes sense because there may exist some outliers​ (maybe much greater or much less than the rest of the​ data) in the data items.
D.
The statement does not make sense because the mean is the true center of the data.

Answer 1

C. The statement makes sense because there may exist some outliers (maybe much greater or much less than the rest of the data) in the data items.

Explanation: The mean is sensitive to extreme values and does not convey how spread out the data are. Without knowing variability (range, interquartile range, standard deviation), a mean can be misleading about a "typical" value. For example, incomes {30k, 31k, 32k, 2,000,000} have mean ≈ 523,250, which does not represent the typical income — an outlier inflates the mean. The median and measures of spread help give a fuller picture.