Chapter 3: Descriptive Measures

Pizza Diameters. In the article, "Assessing Claims Made by a Pizza Chain" by P. Dunn, (Journal of Statistics Education, Vol. 20, No. 1. Pp. 1-19), a sample of pizzas from Domino's was collected. The intention of the study was to test the claim of a local pizza shop that its pizzas are bigger than Domino's. The following table gives the diameters, in centimeters (cm), of 41 large Supreme pizzas from Domino's.

$\begin{array}{lllllll}29.40& 27.45& 26.38& 26.50& 26.55& 26.64& 26.87\\ 26.61& 29.33& 26.67& 26.09& 29.32& 27.12& 26.83\\ 27.04& 29.17& 27.14& 27.04& 29.19& 26.26& 26.16\\ 26.70& 28.78& 29.33& 27.27& 28.90& 29.14& 29.27\\ 28.32& 27.12& 27.05& 28.44& 26.97& 27.52& 26.79\\ 26.54& 26.70& 28.79& 28.97& 28.84& 26.71& \end{array}$

In the below exercise:

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. construct and interpret a boxplot.

Pizza Diameters. In the article, "Assessing Claims Made by a Pizza Chain" by P. Dunn, (Journal of Statistics Education, Vol, $20$, No. $1$. pp. $1-19$), a sample of pizzas from Domino's was collected. The intention of the study was to test the claim of a local pizza shop that its pizzas are bigger than Domino's. The following table gives the diameters, in centimeters (cm), of $41$large Supreme pizzas from Domino's.

Water Park Attendance. Water parks are a huge summer attraction for vacationers in the United States. The Global Attraction Attendance Report, published by the Themed Entertainment Association, provides the attendance report for theme parks and water parks around the world. The following table provides the total yearly attendance for the top $20$water parks in the United States, in thousands during one year.

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. construct and interpret a boxplot.

Nicotine Patches. In the paper "The Smoking Cessation Efficacy of Varying Doses of Nicotine Patch Delivery Systems $4$to $5$Years Post-Quit Day" (Preventative Medicine, $28$. pp. $113-118$) D. DAUGHTON CT al discussed the long-term effectiveness of transdermal nicotine patches on participants who had previously smoked at least $20$cigarettes per day. A sample of $15$participants in the Transdermal Nicotine Study Group (TNSG) reported that they now smoke the following number of cigarettes per day.

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. construct and interpret a boxplot.

Starting Salaries. The National Association of Colleges and Employers (NACE) conducts surveys of salary offers to new college graduates and publishes the results in Salary Survey. The following diagram provides boxplots for the starting annual salaries in thousands of dollars, obtained from samples of $35$business graduates (top boxplot) and $32$education graduates (bottom boxplot). Use the boxplots to compare the starting salaries of the sampled business graduates and education graduates. paying special attention to center and variation.

Obesity. Researchers in obesity wanted to compare the effectiveness of dieting with exercise against dieting without exercise. Seventy-three patients were randomly divided into two groups. Group $1$. composed of $37$patients, was put on a program of dieting with exercise. Group $2$. composed of $36$patients, dieted only. The results for weight loss, in pounds, after $2$months are summarized in the following boxplots. The top boxplot is for Group $1$. and the bottom boxplot is for Group $2$. Use the boxplots to compare the weight losses for the two groups, paying special attention to center and variation.

Consider these sample data:$x_1=12,x_2=8,x_3=9,x_4=17$

a) Find $n$.

b) Compute $\sum x_i$.

c) Determine$\stackrel{-}{x}$.

Cuckoo Care. Many species of cuckoos are brood parasites. The females lay their eggs in the nests of smaller bird species, who then raise the young cuckoos at the expense of their own young. Data on the lengths, in millimeters ($mm$), of cuckoo eggs found in the nests of three bird species - the Tree Pipit. Hedge Sparrow, and Pied Wagtail - were collected by the late O.M. Latter in $1902$and used by L.H.C. Tippett in his text The Methods of States (New York Wiley, $1952$. p. $176$). Use the following boxplots to compare the lengths of cuckoo eggs found in nests of the three bird species, paying special attention to center and variation.

Sickle Cell Disease. A study published by E. Anionwu et al. in the British Medical Journal (Vol. $282$, pp. $283-286$) examined the steady-state hemoglobin levels of patients with three different types of sickle cell disease: HB SC. HB SS. and HB ST. Use the following boxplots to compare the hemoglobin levels for the three groups of patients, paying special attention to center and variation.

Women Students. The US Department of Education sponsors a report on educational institutions, including colleges and universities, titled Digest of Education Statistics. Among many of the statistics provided are the numbers of men and women enrolled in $2year$and $4year$degree-granting institutions. During one year, the percentage of full-time enrolled students that were women, for each of the $50$states and the District of Columbia, is as presented on the WeissStats site.

a. obtain and interpret the quartiles.

b. determine and interpret the interquartile range.

e. find and interpret the five-number summary

d. identify potential outliers, if any.

e. obtain and interpret boxplot.