32 Chapter 2:Descriptive Statistics
FIGURE 2.10 Histogram of a data set skewed to the left.
FIGURE 2.11 Histogram of a data set skewed to the right.
Suppose thatx ̄andsare the sample mean and sample standard deviation of an approxi-
mately normal data set. The following rule, known as theempirical rule, specifies the
approximate proportions of the data observations that are withins,2s, and 3sof the
sample meanx ̄.
The Empirical Rule
If a data set is approximately normal with sample meanx ̄and sample standard deviation
s, then the following statements are true.
- Approximately 68 percent of the observations lie within
̄x±s- Approximately 95 percent of the observations lie within
x ̄± 2 s