Question

two sets of data have the same measures of central tendency. are the data sets the same? explain.

Explanation:

Measures of central tendency (mean, median, mode) summarize data, but they don't capture the full data distribution (like spread or individual values). For example, data sets {1, 3, 5} and {2, 3, 4} have the same median (3) and mean (3), but different values. So same central tendency doesn't mean identical data sets.

Answer:

No, the data sets are not necessarily the same. Measures of central tendency (e.g., mean, median, mode) only describe the "center" of data. Two data sets can have the same central tendency but differ in other aspects like data spread (e.g., range, standard deviation) or individual data points. For example, {1, 3, 5} and {2, 3, 4} both have a mean and median of 3 but contain different values.