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

• A. The data set must contain at least $100$ observations.
• B. The data set must be approximately normally distributed.
• C. The data set must have a mean of $0$.
• D. The data set must have equal minimum and maximum values.

Answer: (B)

Verified step by step guidance

1. Understand that the empirical rule is a statistical guideline that applies to data sets with a specific shape, particularly the normal distribution.
2. Recall that the empirical rule states that for a normal distribution, approximately 68% of data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
3. Recognize that the empirical rule requires the data to be approximately normally distributed because it relies on the symmetrical bell-shaped curve properties of the normal distribution.
4. Note that the number of observations (such as 100) or the mean being zero are not requirements for the empirical rule to hold; the shape of the distribution is the key factor.
5. Conclude that before applying the empirical rule, you must verify or assume that the data set is approximately normally distributed.