Question

which of the following statements must be true? i. the median of data set a is equal to the median of data set b. ii. the standard deviation of data set a is equal to the standard deviation of data set b. a i and ii b i only c ii only d neither i nor ii

Explanation:

Step1: Recall definitions

Median is the middle - value when data is ordered. Standard deviation measures the amount of variation or dispersion of a set of values. There is no general rule that the median of one data - set is equal to the median of another data - set, nor that the standard deviation of one data - set is equal to the standard deviation of another data - set.

Step2: Analyze statements

Statement I: Just because we have two data - sets does not mean their medians are equal. Different distributions of data can lead to different medians.
Statement II: Similarly, standard deviation depends on the individual data points and their deviation from the mean. Two different data - sets are not guaranteed to have the same standard deviation.

Answer:

D. Neither I nor II