Question

determine whether the following statement makes sense or does not make sense, and explain the reasoning.
the mean can be misleading if you dont know the spread of data items.
choose the correct answer below.
a. the statement does not make sense because the mean is the true center of the data.
b. the statement does not make sense because the mean measures the spread of the data items.
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.
d. the statement makes sense because mean is not always the true average of the data.

Explanation:

The statement "The mean can be misleading if you don't know the spread of data items" makes sense. Outliers (values much higher or lower than most data) can skew the mean. For example, in a data set like {1, 2, 3, 4, 100}, the mean is $\frac{1 + 2 + 3 + 4 + 100}{5}=\frac{110}{5} = 22$, but most values are much lower. If we don't know the spread (like the range, standard deviation, or if outliers exist), the mean might give a false impression of the data's center. Option C explains this: the statement makes sense because outliers (much greater or less than other data) can exist, affecting the mean's representation. Option A is wrong because the mean isn't always the "true center" (outliers can skew it). Option B is wrong because the mean measures central tendency, not spread. Option D is wrong because the mean is a type of average (arithmetic mean), so saying it's "not always the true average" is incorrect.

Answer:

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.