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

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

Answer: (B)

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 follow a normal distribution, which is symmetric and bell-shaped.
3. Note that the empirical rule does not require the mean to be zero; the mean can be any value as long as the distribution is normal.
4. Understand that the data set does not need to contain only positive values; normal distributions can include negative values as well.
5. Conclude that the key characteristic required to apply the empirical rule is that the data set must be approximately normally distributed.