Chapter 3: Descriptive Measures

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

Chinchillidae Range. The family of mammals called Chinchillidae contains the chinchilla and viscachas, which are large South American rodents. The article. "Species Richness and Distribution of Neotropical Rodents, with Conservation Implications" (Mammalia Vol. $77$, Issue $1$. pp. $1-19$) by G. Amori et al reports the range sizes of each species of Chinchilladac. There are six species in the Chinchillidae family and the size of each species range, in square kilometers ($k{m}^2$) is given in the following table.

a. Obtain and interpret the population mean range of Chinchilladae species

b. Obtain and interpret the population standard deviation of the ranges of Chinchilladae species.

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

Find the

a. Mean b. median c. mode

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

Tornado Touchdowns:Each year, tomadoes that touchdown are recorded by the Storm Prediction Center and published in Monthly Tom Statistics. The following table gives the number of tomados that touched down in the United States during each month of one year.

$$\begin{gathered} 324711820497 \\ 688662579899 \end{gathered}$$

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

STD Surveillance. The Centers for Disease Control and Prevention compiles reported cases and rates of diseases in United States cities and outlying areas. In a document titled Sexually Transmitted Disease Surveillance, the number of reported cases of all stages of syphilis is provided for cities, including Orlando, Florida, and Cincinnati, Ohio. Following is the number of reported cases of syphilis for those two cities over the years $2007-2011$.

a. Obtain the individual population means the number of cases for both cities.

b. Without doing any calculations, decide for which city the population standard deviation of the number of cases is smaller. Explain your answer.

c. Obtain the individual population standard deviations of the number of cases for both cities.

d. Are your answers to parts (b) and (c) consistent? Why or why not?

Dart Doubles. The top two players in the $2001-2002$Professional Darts Corporation World Championship were Phil Taylor and Peter Manley Taylor and Manley dominated the competition with a record number of doubles. A double is a throw that lands in either the outer ring of the dartboard or the outer ring of the bulls-eye. The following table provides the number of doubles thrown by each of the two players during the five rounds of competition, as found in Chance (Vol. $18$. No. $3$. pp. $48-55$)

a. Obtain the individual population means of the number of doubles.

b. Without doing any calculations, decide for which player the standard deviation of the number of doubles is smaller. Explain your answer.

c. Obtain the individual population standard deviations of the number of doubles.

d. Are your answers to parts (b) and (c) consistent. Why or why not?

Doing Time. According to the Compendium of Federal Justice Statistics, published by the Bureau of Justice Statistics, the meantime served to first release by Federal prisoners is $32.9$months. Assume the standard deviation of the times served is $17.9$months. Let $x$denote time served to first release by a Federal prisoner.

a. Find the standardized version of $x$.

b. Find the mean and standard deviation of the standardized variable.

c. Determine the $z$-scores for prison times served of $81.3$months and $20.8$months. Round your answers to two decimal places.

d. Interpret your answers in part (c)

e. Construct a graph similar to Fig. $3.20$on page $146$that depicts your results from parts (b) and (c)

Gestation Periods of Humans. Gestation periods of humans have a mean of $266$days and a standard deviation of $16$days. Let $y$denote the variable "gestation period" for humans.

a. Find the standardized variable corresponding to $y.$

b. What are the mean and standard deviation of the standardized variable?

c. Obtain the z-scores for gestation periods of 227 days and 315 days. Round your answers to two decimal places.

d. Interpret your answers in part (c).

e. Construct a graph similar to Fig. 3.20 on page 146 that shows your results from parts (b) and (c).

Gestation Periods of Humans. Gestation periods of humans have a mean of $266$days and a standard deviation of $16$days. Let $y$denote the variable "gestation period" for humans.

a. Find the standardized variable corresponding to$y$

b. What are the mean and standard deviation of the standardized variable?

c. Obtain the $z$-scores for gestation periods of $227$days and $315$days. Round your answers to two decimal places.

d. Interpret your answers in part (c).

c. Construct a graph similar to Fig. 3.20 on page 146 that shows your results from parts (b) and (c).