A First Course in Statistics, 12th Edition

2.5 Using the Mean and Standard Deviation to Describe Data

We’ve seen that if we are comparing the variability of two samples selected from a population, the sample with the larger standard deviation is the more variable of the two. Thus, we know how to interpret the standard deviation on a relative or comparative basis, but we haven’t explained how it provides a measure of variability for a single sample.

Teaching Tip

Use data collected in class to generate similar intervals and find the proportion of the class that falls into each interval.

To understand how the standard deviation provides a measure of variability of a data set, consider the following questions: How many measurements are within one standard deviation of the mean? How many ...