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Chapter 3: Q. 3.150 (page 136)
Explain why minimum and maximum observations are added to the three quartiles to describe better the variation in a data set.
The minimum and maximum observations are added because their difference denotes the variation in data.
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The Beatles. In the article. "Length of The Beatles' Songs",(Chance Vol. . No. , pp. ). T. Koyama discusses aspects and interpretations of the lengths of songs by The Beatles. Data on the length, in seconds, of Beatles' songs are presented on the Weiss Stats site.
Hospital Stays. The U.S. National Center for Health Statistics compiles data on the length of stay by patients in short-term hospitals and publishes its findings in Vital and Health Statistics, A random sample of 21 patients yielded the following data on length of stay, in days.
a. obtain and interpret the quartiles.
b. determine and interpret the interquartile range.
c. find and interpret the five-number summary:
d. identify potential outliers, if am:
e. construct and interpret a boxplot.
Complete the following statement: The descriptive measure is resistant if .......
Objects such as asteroids and comets that come into proximity with the Earth are called near-Earth objects (NEOs). The National Aeronautics and Space Administration (NASA) tracks and catalogues all NEOs that are at least kilometer wide. Data on NEOs can be found on the NASA website; The following table gives the relative velocities in kilometers per second , arranged in increasing order, for the NEO close approaches to the earth during June .
The sample mean and sample standard deviation of these velocities are and respectively.
a. Compare the percentage of the observations that actually lie within two standard deviations to either side of the mean with that given by Chebyshev's rule with
b. Repeat part (a) with
c. Interpret your results from parts (a) and (b).
Consider the data set: .
a) Obtain the mean and median of the data.
b) Replace the in the data set by and again compare the mean and median. Decide which measure of the center works better here and explain your answer.
c) For the data set in part b) the mean is neither central nor typical for the data. The lack of what property of the mean accounts for this result.
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