Descriptive Measures

Determine the age and sample standard deviation for each of the due sets. For the sample standard deviation round each answer to one more decimal place than that used for the observation. 

Tornado Touchdowns. Each year, tornadoes that touch down are recorded by the Storm Prediction Center and published in Months Tomade Statistics. The following table gives the number of tornadoes that touched down in the United States during each month of one year [SOURCE: National Oceanic and Atmospheric Administration  

Regarding$z$-scores:
a. How is a $z$-score obtained?
b. What is the interpretation of a $z$-score?
c. An observation has a $z$-score of $2.9$. Roughly speaking, what is the relative standing of the observation?

Explain in detail the purpose of a measure of center.

Name and describe the three most important measures of center.

Of the mean, median and mode which is the only one appropriate for use with quantitative data.

True of False: The mean, median and mode can all be used with quantitative data. Explain your answer.

Consider the data set: $1,2,3,4,5,6,7,8,9$.

a) Obtain the mean and median of the data.

b) Replace the $9$ in the data set by $99$ 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.

Complete the following statement: The descriptive measure is resistant if .......

Floor space: The U.S department housing and urban development compiles information on new, privately owned single family houses. According to the document in 2012 the mean floor space of such homes are $2505 sq ft$ and the median was $2306 sq ft$. Which measure of center do you think is more appropriate? Justify your answer.

Net worth: The board of Governors of the Federal Reserve system publishes information on family net worth in the survey of consumers fiances. In$2012$ the mean net worth of the families in the united state was  $\backslash (498.8$ thousand and the median net worth was  $\backslash )77.3$ thousand. Which measure of center do you think is more appropriate? Justify your answer.

We have provided simple data set for you to practices the basics of  finding measures of center. For each data set determine the:

a) Mean 

b)Median

c) Mode.

The given data set is $4,0,5$.

We have provided simple data set for you to practices the basics of  finding measures of center. For each data set determine the:

a) Mean 

b)Median

c) Mode.

The given data set is $3,5,7$

We have provided simple data set for you to practices the basics of  finding measures of center. For each data set determine the:

a) Mean 

b)Median

c) Mode.

The given data set is $1,2,4,4$.

We have provided simple data set for you to practices the basics of  finding measures of center. For each data set determine the:

a) Mean 

b)Median

c) Mode.

The given data set is: $2, 5, 0, -1$

We have provided simple data set for you to practices the basics of  finding measures of center. For each data set determine the:

a) Mean 

b)Median

c) Mode.

The given data set is:$1, 9, 8, 4, 3$.

We have provided simple data set for you to practices the basics of  finding measures of center. For each data set determine the:

a) Mean 

b)Median

c) Mode.

The given data set is: $4,2,0,2,2$.

Explain what each of symbol represents:

$a)\sum _{} b) n c)\stackrel{-}{x}$

For a particular population is the population mean a variable? What about a sample mean?

Consider these sample data: $x_1=1, x_2=7,x_3=4,x_4=5, x_5=10$

a) Find $n$

b) Compute $\sum x_i$

c) Determine $\stackrel{-}{x}$.

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 $\stackrel{-}{x}$.

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. 

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

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. 

Hurricanes. An article by D. Schaefer et al. reported on a long-term study of the effects of hurricanes on tropical streams of the Luquillo Experinental Forest in Puerto Rico. The study shows that Hurricane Hugo had a significant impact on stream water chemistry. The following table shows a sample of $10$ammonia fluxes in the first year after Hugo. Data are in kilograms per hectare per year.

$96, 116, 66, 57, 147, 54, 147, 88, 175, 154$

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.

$$\begin{gathered} 3 2 47 118 204 97 \\ 68 86 62 57 98 99 \end{gathered}$$

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.

Technical Merit. In one Winter Olympics, Michelle Kwan competed in the Short Program ladies singles event. From nine judges, she received scores ranging from I (poor) to 6 (perfect). The following table provides the scores that the judges gave her on technical merit, found in an article by S. Berry .

$5.8 5.7 5.9 5.7 5.5 5.7 5.7 5.7 5.6$

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.

Billionaires' Club. Each year, Forbes magazine compiles a list of the $400$richest Americans. As of September $19, 2012$, the top 10 on the list are as shown in the following table.

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.

Tablet Computers. Tablet personal computers such as iPad and Kindle Fire are one piece portable computers that typically offer a touchscreen. Tablets are available in different sizes but generally offer a screen that is greater than 7 inches diagonally. Consumer Reports reviews tablets of different sizes and Internet capabilities The battery lives, in hours, for a sample of tablets with screen sizes between 9 and 12 inches are provided in the following table. 

$8.4 5.6 10.9 10.8 11.5 8.0 8.5 129$

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.

 The Beatles. The English rock band, The Beatles, was formed in Liverpool in $1960$. There are $12$ studio albums that are considered part of their core catalogue. In the article, "Length of The Beatles Songs" . T. Koyama lists the album title, date of release, and number of songs on each album. Here are the album names and numbers of songs.

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

Medieval Cremation Burials. In the article "Material Cul ture as Memory: Combs and Cremations in Early Medieval Britain (Early Medieval Europe, Vol. 12. Issue 2. pp. 89-128), H. Williams discussed the frequency of cremation burials found in 17 archaeological sites in eastem England. Here are the data. 

$$\begin{gathered} 83 64 46 523 35 34 265 2484 \\ 46 385 21 86 429 51 258 119 \end{gathered}$$

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

Monthly Motorcycle Casualties. The Scottish Executive, Analytical Services Division Transport Statistics, compiles data on motorcycle casualties. During one year, monthly casualties from motorcycle accidents in Scotland for built-up roads and non-built-up roads were as follows 

a) Find the mean, median, and mode of the number of motorcycle casualties for built-up roads.

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.

 Daily Motorcycle Accidents. The Scottish Executive, Analy. tical Services Division Transport Statistics, compiles data on motor cycle accidents. During one year, the numbers of motorcycle accidents in Scotland were tabulated by day of the week for built-up roads and non-built-up roads and resulted in the following data .

a. Find the mean and median of the number of accidents for built-up roads. 

Honeymoons. Popular destination for the newlyweds of today are the Caribbean and Hawaii. According to a recent American Wedding Study by the Conde Nat Bridal Group, a honeymoon, on a average, lasts 9.4 days and costs $5111. A sample of newlyweds reported the following lengths of stay of their honeymoons

Part (a) find $n$

Part (b) Compute $\sum _{}{x}_i$

Part (c) Determine the sample mean. Round your answer to one more decimal place than that used for the observation.

Sleep. In 1908. W.S Gosset published the article " The probable Error of a mean" ( Biometrika, vOL.6, pp. 1-25) In this pioneering paper written under the pseudonym "Student" Gosset introduced What later became known as Student's t distribution which we discuss in a later chapter. Gosset used the following dataset, which shown the additional sleep in hours obtained by a sample of 10 patients given laevohysocyamine hydrobromide. 

Part (a) find $n$

Part (b) Compute

Part (c) Determine the sample mean. Round your answer to one more decimal place than that used for the observation.

Pesticides in Pakistan Pesticides are chemical often used in agriculture to control pests. In Pakistan, 70% of the population depends on agriculture, and pesticide use there has increased rapidly. In the article, "Monitoring Pesticide Residues in Fresh Fruits Marketed in Peshawar, Pakistan" ( American Laboratory, Vol.37, No. 7, pp. 22 to 24) J. Shah et al. sampled the most commonly used fruit in Pakistan and analyzed pesticide residues in the fruit. The amounts, in mg/kg, of the pesticide Dichlorovos for a sample of apples, guavas, and mangos were as follows

Part (a) find $n$

Part (b) Compute $\sum _{}{x}_i$

Part (c) Determine the sample mean. Round your answer to one more decimal place than that used for the observation.

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.

Router Horsepower. In the article "Router Roundup" T. Kleck reported on tests of seven fixed-base routers for performance, features, and thandling. The following table gives the horsepower (hp) for each of the seven routers tested. 

$1.75 2.25 2.25 2.25 1.75 2.00 1.50$

a) Determine the mode of the data. 
b) Decide whether it would be appropriate to use either the mean or median as a measure of center. Explain your answer. 

 NCAA Wrestling Champ. From NCAA. com the official Web site for NCAA sports we obtained the National Collegiate Athletic Association wrestling champions for the years $1989-2013$ in the document "Championship History". They are displayed in the following table.

a) Determine the mode of the data. 
b) Decide whether it would be appropriate to use either the mean or median as a measure of center. Explain your answer .

Road Rage. The report Controlling Road Rage: A Literature Review and Pilot Study was prepared for the AAA Foundation for Traffic Safety by D. Rathbone and J. Huckabee. The authors dis cussed the results of a literature review and pilot study on how to prevent aggressive driving and road rape. As described in the study druge is criminal behavior by motorists characterized by uncontrolled anger that results in violence or threatened violence on the road. One of the goals of the study was to determine when road mare occurs most often. The days on which 69 road rage incidents occurred are presented in the following table. 

a) Determine the mode of the data. 
b) Decide whether it would be appropriate to use either the mean or median as a measure of center. Explain your answer. 

U.S. Supreme Court Justices. From We found that the law schools of the justices of the US Supreme Court, as of September 9, 2011, are as follows 

a) Determine the mode of the data. 
b) Decide whether it would be appropriate to use either the mean or median as a measure of center. Explain your answer.  

 Robbery Locations. The Department of Justice and the Federal Bureau of Investigation publish a compilation on crime statistics for the United States in Crime in the United States. The following table provides a frequency distribution for robbery type during a one-year period .

a) Determine the mode of the data. 
b) Decide whether it would be appropriate to use either the mean or median as a measure of center. Explain your answer. 

Freshmen Politics. The Higher Education Research Institute of the University of California, Los Angeles, publishes information on characteristics of incoming college freshmen in the America. Freshman. In $2000, 27.7\%$ of incoming freshmen characterized their political views as liberal. $51.9\%$ as moderate, and $20.4\%$ as conservative. For this year, a random sample of $500$incoming college freshmen yielded the following frequency distribution for political views .

a) Determine the mode of the data. 
b) Decide whether it would be appropriate to use either the mean or median as a measure of center. Explain your answer.  

Medical School Faculty. The Association of American Medical College (AAMC) in a compiles data on medical school facility and publishes the results in AAMC Faculty Roster. The following table presents a frequency distribution of rank for medical school faculty during one year. 

a) Determine the mode of the data. 
b) Decide whether it would be appropriate to use either the mean or median as a measure of center. Explain your answer.  

An Edge in Roulette! An American roulette wheel contains$18$ red numbers, $18$ black numbers, and $2$ green numbers. The following the shows the free with which the hall landed on each color in $200$ trials.

U.S Supreme Court Justices. From Wikipedia, we found that the ages of the justices of the U.S Supreme Court, as of September 9, 2013, are as follows, in year.

Part (a) find $n$

Part (b) Compute $\sum _{}{x}_i$

Part (c) Determine the sample mean. Round your answer to one more decimal place than that used for the observation.

Food Choice. As you discovered earlier, ordinal data are data about order or rank given on a scale such as 1,2,3,..... or A,B,C..... Most statisticians recommend using the median to indicate the center of an ordinal data set, but some researchers also use the mean. In the paper " Measurement of Ethical Food Choice motives" (Appetite. Vol 34,pp. 55 - 59). research psychologists M. Lindeman and M Vaananen of the University of Helsinki published a study on the factor that most influence people's choice of food. One of the question asked of the participants was how important, on a scale of 1 to 4 (1 = not at all important, 4 = very important), is a scale of welfare in food choice motive, Where ecological welfare includes animal welfare and environmental protection. Here are the ratings given by 14 of the participants.

Part (a) Computer the mean of the data.

Part (b) Computer the median of the data.

Part (c) Decide which of the two measures of center is best.

In each of Exercises 3.42-3.50, use the technology of your choice to obtain the measures of center that are appropriate from among the mean, median, and mode. Discuss your results and decide which measure of center is most appropriate. Provide a reason for your answer. Note: If an exercise contains more than one data set, perform the aforementioned tasks for each data set. 

Japanese Vehicle Exports. The Japan Automobile Manufacturer's Association provides data on exported vehicles in Motor Vehicle Statistics of Japan. In 2010, cars, trucks, and buses constituted 88.3%, 9.3%, and 2.4% of vehicle exports, respectively. A random sample of last year's exports yielded the vehicle-type data on the WeissStats site.

In each of Exercises 3.42-3.50, use the technology of your choice to obtain the measures of center that are appropriate from among the mean, median, and mode. Discuss your results and decide which measure of center is most appropriate. Provide a reason for your answer. Note: If an exercise contains more than one data set, perform the aforementioned tasks for each data set. 

 U.S. Hospitals. The American Hospital Association conducts annual surveys of hospitals in the United States and publishes its findings in AHA Hospital Statistics. Data on hospital type for U.S. registered hospitals can be found on the WeissStats site. For convenience we use the following abbreviations:

• NPC: Nongovernment not-for-profit community hospitals 
• IOC: Investor-owned (for-profit) community hospitals 
• SLC: State and local government community hospitals
• FGH: Federal government hospitals. NFP: Nonfederal psychiatric hospitals. 
• NLT: Nonfederal long-term-care hospitals. 
• HUI: Hospital units of institutions

In each of Exercises 3.42-3.50, use the technology of your choice to obtain the measures of center that are appropriate from among the mean, median, and mode. Discuss your results and decide which measure of center is most appropriate. Provide a reason for your answer. Note: If an exercise contains more than one data set, perform the aforementioned tasks for each data set. 

Marital Status and Drinking. Research by W. Clark and L. Midanik (Alcohol Consumption and Related Problems: Alcohol and Health Monograph 1. DHHS Pub. No. (ADM) 82-1190) examined, among other issues, alcohol consumption patterns of U.S. adults by marital status. Data for marital status and number of drinks per month, based on the researchers ' survey results, are provided on the WeissStats site.

In each of Exercises 3.42-3.50, use the technology of your choice to obtain the measures of center that are appropriate from among the mean, median, and mode. Discuss your results and decide which measure of center is most appropriate. Provide a reason for your answer. Note: If an exercise contains more than one data set, perform the aforementioned tasks for each data set.

Ballot Preferences. In Issue 338 of the Amstat News, then president of the American Statistical Association Fritz Scheuren reported the results of a survey on how members would prefer to receive ballots in annual elections. On the WeissStats site, you will find data for preference and highest degree obtained for the 566 respondents.

In each of Exercises 3.42-3.50, use the technology of your choice to obtain the measures of center that are appropriate from among the mean, median, and mode. Discuss your results and decide which measure of center is most appropriate. Provide a reason for your answer. Note: If an exercise contains more than one data set, perform the aforementioned tasks for each data set.

The Great White Shark. In an article titled "Great White Deep Trouble" (National Geographic, Vol. 197 (4), 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. 

In each of Exercises 3.42-3.50, use the technology of your choice to obtain the measures of center that are appropriate from among the mean, median, and mode. Discuss your results and decide which measure of center is most appropriate. Provide a reason for your answer. Note: If an exercise contains more than one data set, perform the aforementioned tasks for each data set.

High School Completion. As reported by the U.S. 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 WeissStats site.