# Question: Consider the data sets portrayed in Figs 3 5 and 3 6

Consider the data sets portrayed in Figs. 3.5 and 3.6 on page 108.

a. Chebychev’s rule says that at least 75% of the observations lie within two standard deviations to either side of the mean. What percentage of the observations portrayed in Fig. 3.5 actually lie within two standard deviations to either side of the mean?

b. Chebychev’s rule says that at least 89% of the observations lie within three standard deviations to either side of the mean. What percentage of the observations portrayed in Fig. 3.5 actually lie within three standard deviations to either side of the mean?

c. Repeat parts (a) and (b) for the data portrayed in Fig. 3.6.

d. From parts (a)–(c), we see that Chebychev’s rule provides a lower bound on, rather than a precise estimate for, the percentage of observations that lie within a specified number of standard deviations to either side of the mean. Nonetheless, Chebychev’s rule is quite important for several reasons. Can you think of some?

a. Chebychev’s rule says that at least 75% of the observations lie within two standard deviations to either side of the mean. What percentage of the observations portrayed in Fig. 3.5 actually lie within two standard deviations to either side of the mean?

b. Chebychev’s rule says that at least 89% of the observations lie within three standard deviations to either side of the mean. What percentage of the observations portrayed in Fig. 3.5 actually lie within three standard deviations to either side of the mean?

c. Repeat parts (a) and (b) for the data portrayed in Fig. 3.6.

d. From parts (a)–(c), we see that Chebychev’s rule provides a lower bound on, rather than a precise estimate for, the percentage of observations that lie within a specified number of standard deviations to either side of the mean. Nonetheless, Chebychev’s rule is quite important for several reasons. Can you think of some?

**View Solution:**## Answer to relevant Questions

Consider the following sample of exam scores, arranged in increasing order. The sample mean and sample standard deviation of these exam scores are, respectively, 85 and 16.1. a. Use Chebychev’s rule to obtain a lower bound ...The National Center for Health Statistics publishes information on the duration of marriages in Vital Statistics of the United States. Which measure of center is more appropriate for data on the duration of marriages, the ...From the Fatality Analysis Reporting System (FARS) of the National Highway Traffic Safety Administration, we obtained data on the numbers of traffic fatalities in Wisconsin and New Mexico for the years 1982-2003. Use the ...Philosophical and health issues are prompting an increasing number of Taiwanese to switch to a vegetarian lifestyle. In the paper "LDL of Taiwanese Vegetarians Are Less Oxidizable than Those of Omnivores" (Journal of ...In the paper "Total Body Composition by Dual-Photon (153Gd) Absorptiometry" (American Journal of Clinical Nutrition, Vol. 40, pp. 834-839), R. Mazess et al. studied methods for quantifying body composition. Eighteen randomly ...Post your question