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The Great Gretzky. Wayne Giretzy, a retired professional hockey player, played 20 seasons in the National Hockey League (NHL), from 1980 through 1999 , S, Berry explored some of Gretaky"s accomplishmeats in "A Statistician Reads the Sports Pages" (Chanee, Vol, 16, Ne, 1. Pp. 49-54). The following table shoras the sumber of games in which Greuky played during each of has 20 seasons in the NHL.

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.

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.

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.

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.

Although, in practice, sample data are generally analyzed in inferential studies, what is ultimate objectives of such studies ?

Fill in the following blanks.

(a) A standardized variable always has mean _____ and standard deviation _______ .

(b) The z-score corresponding to an observed value of a variable tells you ______ .

(c) A positive z-score indicates that the observation is ______ the mean, whereas a negative z-score indicates that the observation is _______ the mean.

Age of U.S. Residents. The U.S. Census Bureau collects information about the ages of people in the United States. Results are published in Current Population Reports

a. Identify the variable and population under consideration.

b. A sample of six U.S. residents yielded the following data on ages (in years). Determine the median of these age data. Decide whether this descriptive measure is a parameter or a statistic, and use statistical notation to express the result.

c. By consulting the most recent census data, we found that the median age of all US residents is $37.2yrs$. Decide whether that descriptive measure is a parameter or a statistic and use statistical notation to express the result

Atlantic Basin Hurricanes. The Tropical Cyclone Report, a publication of the National Hurricane Center, contains comprehensive information on each tropical cyclone, including synoptic history, meteorological statistics, casualties, and damages. A hurricane is a tropical cyclone with winds that have reached a constant speed of $74milesperhour$or more. During one year, there were $10$Atlantic basin hurricanes. Their maximum wind speeds, in miles per hour ($mph$), were as shown in the following table.

Consider these storms a population of interest. Obtain the following parameters for the maximum wind speeds. Use the appropriate mathematical notation for the parameters to express your answers.

a. Mean

b. Standard deviation

c. Median

d. Mode

e. IQR

Dallas Mavericks. From the ESPN website, in the Dallas Mavericks Roster, we obtained the following ages, in years, for the players on that basketball team for the $2013-2014$season.

Obtain the following parameters for these ages. Use the appropriate mathematical notation for the parameters to express your answers.

a. Mean

b. Standard deviation

c. Median

d. Mode

e. IQR