3-2 Measures of Variation 109 especially those that include the topic of hypothesis tests, which are also called tests of significance. The following range rule of thumb is based on the population mean m and the population standard deviation s, but for large and representative samples, we could use x and s instead. Range Rule of Thumb for Identifying Significant Values Significantly low values are m - 2s or lower. Significantly high values are m + 2s or higher. Values not significant: Between 1m - 2s2 and 1m + 2s2 See Figure 3-4, which illustrates the above criteria. Values not significant Significantly low values Significantly high values m m − 2s m + 2s FIGURE 3-4 Range Rule of Thumb for Identifying Significant Values Range Rule of Thumb for Estimating a Value of the Standard Deviation s To roughly estimate the standard deviation from a collection of known sample data, use s ≈ range 4 CAUTION An outcome can be statistically significant, and it may or may not be important. Don’t associate statistical significance with importance. EXAMPLE 4 Range Rule of Thumb for Interpreting s Using the 147 pulse rates of females in Data Set 1 “Body Data” in Appendix B, the mean is 74.0 beats per minute and the standard deviation is 12.5 beats per minute. Use the range rule of thumb to find the limits separating values that are significantly low or significantly high, and then determine whether the pulse rate of 102 beats per minute is significantly high. SOLUTION With a mean of 74.0 and a standard deviation of 12.5, we use the range rule of thumb to find the limits separating values that are significantly low or significantly high, as follows: Significantly low values are 174.0 - 2 * 12.52 or lower, so significantly low values are 49.0 beats per minute or lower. Significantly high values are 174.0 + 2 * 12.52 or higher, so significantly high values are 99.0 beats per minute or higher. Values not significant between 49.0 beats per minute and 99.0 beats per minute INTERPRETATION Based on these results, we expect that typical pulse rates of females are between 49.0 beats per minute and 99.0 beats per minute. Because the given value of 102 beats per minute falls above 99.0 beats per minute, we can consider it to be significantly high. (The Mayo Clinic website states that “a normal resting heart rate for adults ranges from 60 to 100 beats a minute.”) YOUR TURN. Do Exercise 33 “U.S. Presidents.”
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