Chapter 3: Descriptive Measures

The Great White Shark. In an article titled "Great White. Deep Trouble" (National Geographic, Vol. $197\left(4\right)$, pp. $2-29$). Peter Benchley-the author of JAWS-discussed various aspects of the Great White Shark Carcharodon carcharias). Data on the number of pups borne in a lifetime by each of $80$Great White Shark females are provided on the WeissStats site.

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 any.

e. obtain and interpret boxplot.

The Beatles. In the article. "Length of The Beatles' Songs",(Chance Vol. $25$. No. $1$, pp. $30-33$). T. Koyama discusses aspects and interpretations of the lengths of songs by The Beatles. Data on the length, in seconds, of $229$ Beatles' songs are presented on the Weiss Stats site.

High School Completion. As reported by the US Census Bureau in Educational Attainment in the United States, the percentage of adults in each state and the District of Columbia who have completed high school is provided on the Weiss Stats site.

Bachelor's Completion. As reported by the US Census Bureau in Educational Attainment in the United States, the percentage of adults in each state and the District of Columbia who have completed a bachelor's degree is provided on the Weiss Stats site.

Body Temperature. A study by researchers at the University of Maryland addressed the question of whether the mean body temperature of humans is $98.6°F$. The results of the study by P. Mackowiak et al. appeared in the article "A Critical Appraisal of $98.6°F$the Upper Limit of the Normal Body Temperature, and Other Legacies of Carl Reinhold August Wunderlich' (Journal of the American Medical Association, Vol. data-custom-editor="chemistry" $268$, pp. $1578-1580$) Among other data, the researchers obtained the body temperatures of $93$healthy humans, as provided on the Weiss Stats site

Treating Psychotic Illness. L. Petersen et al evaluated the effects of integrated treatment for patients with a first episode of psychotic illness in the paper "A Randomized Multicenter Trial of Integrated Versus Standard Treatment for Patients with a First Episode of Psychotic Illness" (British medical journal, vol. $331$$.\left(7517\right):602$). Part of the study included a questionnaire that was designed to measure client satisfaction with both the integrated treatment and standard treatment. The data on the Weiss Stats site is based on the results of the client questionnaire.

(a) Use the technology of your choice to obtain boxplots for the data sets, using the same scale.

(b) Compare the data sets by using your results from part(a) paying special attention to center and variation

The Etruscans. Anthropologists are still trying to unravel the mystery of the origins of the Etruscan empire, a highly advanced Italic civilization formed around the eighth century B.C. in central Italy. Were they native to the Italian peninsula or, as many aspects of their civilization suggest, did they migrate from the East by land or sea? The maximum head breadth, in millimeters, of $70$modern Italian male skulls and that of $84$preserved Etruscan male skulls were analyzed to help researchers decide whether the Etruscans were native to Italy. The resulting data can be found on the WeissStats site. [SOURCE: N. Barnicot and D. Brothwell, "The Evaluation of Metrical Data in the Comparison of Ancient and Modern Bones." In Medical Biology and Etruscan Origins, G. Wolstenholme and C. O'Connor, cds., Littlc, Brown \& Co., $1959$]

Find the

a. Mean b. median c. models

For the mean and the median, round each answer to one more decimal place than that used for the observations.

Amphibian Embryos. In a study of the effects of radiation on amphibian embryos titled "Shedding Light on Ultraviolet Radiation and Amphibian Embryos" L. Licht recorded the time it took for a sample of seven different species of frogs' and toads' eggs to hatch. The following table shows the times to hatch, in days.

$6,7,11,6,5,5,11$

Prolonging Life. Vitamin $C$(ascorbate) boosts the human immune system and is effective in preventing a variety of illnesses. In a study by E. Cameron and L. Pauling titled "Supplemental Ascorbate in the Supportive Treatment of Cancer; Reevaluation of Prolongation of Survival Times in Terminal Human Cancer" (Proceedings of the National Acadeny of Seience, Vol. $75$, No. $9$, pp. $4538-4542$), patients in advanced stages of cancer were given a vitamin $C$supplement. Patients were grouped according to the organ affected by cancer: stomach, bronchus, colon, ovary, or breast. The study yielded the survival times, in days, given on the WeissStats site.

Identify each quantity as a parameter or a statistic

(a) $\mu$ (b)$s$ (c)$\overline{x}$ (d)$\sigma$