Section 3.2 Summary

1. The simplest measure of variability, or measure of spread, is the range. The range is simply the difference between the maximum and minimum values in a data set, but the range has drawbacks because it relies on the two most extreme data values.
2. The variance and standard deviation are measures of spread that utilize all available data values. The population variance can be thought of as the mean squared deviation. The standard deviation is the square root of the variance. We interpret the value of the standard deviation as the typical deviation, that is, the typical distance between a data value and the mean.
3. The variance and standard deviation may also be calculated for a sample. Again, we interpret the value of the standard deviation as the typical deviation, that is, the typical distance between a data value and the mean.
4. For bell-shaped distributions, the Empirical Rule may be applied. The Empirical Rule states that, for bell-shaped distributions, about 68%, 95%, and 99.7% of the data values will fall within 1, 2, and 3 standard deviations of the mean, respectively.
5. Chebyshev's Rule allows us to find the minimum percentage of data values that lie within a certain interval. Chebyshev's Rule states that the proportion of values from a data set that will fall within standard deviations of the mean will be at least , where .