Which characteristic must be known about a data set before the empirical rule can be applied?

• A. The data set must have an equal number of even and odd values.
• B. The data set must have a mean of $0$.
• C. The data set must be approximately normally distributed.
• D. The data set must contain only positive values.

Answer: (C)

Verified step by step guidance

1. Understand that the empirical rule, also known as the 68-95-99.7 rule, describes the percentage of data within one, two, and three standard deviations from the mean in a data set.
2. Recognize that the empirical rule applies specifically to data sets that are approximately normally distributed, meaning the data follows a bell-shaped curve symmetric around the mean.
3. Note that the empirical rule does not require the data to have an equal number of even and odd values, nor does it require the mean to be zero or the data to contain only positive values.
4. Therefore, before applying the empirical rule, verify that the data set is approximately normally distributed by checking its shape using graphical methods (like histograms or Q-Q plots) or statistical tests for normality.
5. Once normality is confirmed, you can confidently use the empirical rule to estimate the proportion of data within certain standard deviation ranges from the mean.