Fundamentals of Statistics - Pearson

1 Five Basic Words of Branches of of Selection MethodsOne-Minute SummaryTest YourselfEvery day, you encounter numerical information that describes or analyzessome aspect of the world you live in. For example, here are some news itemsthat appeared in the pages of The New York Timesduring a one-month period: Between 1969 and 2001, the rate of forearm fractures rose 52% for girlsand 32% for boys, with the largest increases among children in earlypuberty, according to a recent Mayo Clinic study. Across the New York metropolitan area, the median sales price of a sin-gle-family home has risen by 75% since 1998, an increase of more than$140,000.

2 A study that explored the relationship between the price of a book andthe number of copies of a book sold found that raising prices by 1%reduced sales by 4% at , but reduced sales by only stories as these would not be possible to understand without Statistics ,the branch of mathematics that consists of methods of processing and ana-lyzing data to better support rational decision-making processes. Using statis-tics to better understand the world means more than just producing a newset of numerical information you must interpretthe results by reflecting onthe significance and the importance of the results to the decision-makingFundamentals ofStatisticsCH01 8:33 AM Page 1process you face.

3 Interpretation also means knowing when to ignore results,either because they are misleading, are produced by incorrect methods, orjust restate the obvious, as this news story reported by the comedian DavidLetterman illustrates:USA Todayhas come out with a new survey. Apparently, 3 out ofevery 4 people make up 75% of the newer technologies allow people to process and analyze ever-increasingamounts of data, Statistics plays an increasingly important part of many deci-sion-making processes today. Reading this chapter will help you understandthe Fundamentals of Statistics and introduce you to concepts that are usedthroughout this Five Basic Words of StatisticsThe five words population, sample, parameter, statistic(singular), and variableform the basic vocabulary of Statistics .

4 You cannot learn much about statis-tics unless you first learn the meanings of these five the members of a group about which you want to draw a All citizens who are currently registered to vote, allpatients treated at a particular hospital last year, the entire daily output of acereal factory s production part of the population selected for registered voters selected to participate in a recent surveyconcerning their intention to vote in the next election, the patients selectedto fill out a patient-satisfaction questionnaire, 100 boxes of cereal selectedfrom a factory s production numerical measure that describes a characteristic of a percentage of all registered voters who intend to vote in thenext election, the percentage of all patients who are very satisfied with thecare they received, the average weight of all the cereal boxes produced on afactory s production line on a particular 1 Fundamentals OF important pointCH01 8.

5 33 AM Page 2 StatisticCONCEPTA numerical measure that describes a characteristic of a percentage in a sample of registered voters who intend tovote in the next election, the percentage in a sample of patients who are verysatisfied with the care they received, the average weight of a sample of cerealboxes produced on a factory s production line on a particular Statistics for a sample is the most commonactivity, because collecting population data is impractical for most actualdecision-making characteristic of an item or an individual that will be analyzedusing , the household income of the citizens who voted in thelast presidential election, the publishing category (hardcover, trade paper-back, mass-market paperback, textbook) of a book, the number of varietiesof a brand of the variables taken together form the data of ananalysis.

6 Although you may have heard people saying that they are analyzingtheir data, they are, more precisely, analyzing their should distinguish between a variable, such as gender, and its valueforan individual, such as male. An observationis all the values for an individualitem in the sample. For example, a survey might contain two variables, gen-der and age. The first observation might be male, 40. The second observationmight be female, 45. The third observation might be female, 55. A variableissometimes known as a column of data because of the convention of enteringeach observation as a unique row in a table of data.

7 (Likewise, you may hearsome refer to an observation as a row of data.)Variables can be divided into the following THE FIVE BASIC WORDS OF STATISTICS3 Categorical Variables Numerical Variables ConceptThe values of these variables are The values of these variablesselected from an established list involve a counted or measuredof categories. value. Subtypes None. Discrete valuesare counts valuesare meas-ures, and any value can theoreti-cally occur, limited only by theprecision of the measuringprocess. (continues)CH01 8:33 AM Page 3 All variables should have an operational definition that is, a universally-accepted meaning that is clear to all associated with an analysis.

8 Withoutoperational definitions, confusion can occur. A famous example of such con-fusion was the tallying of votes in Florida during the 2000 presidentialelection in which, at various times, nine different definitions of a valid ballotwere used. (A later analysis1determined that three of these definitions,including one pursued by Al Gore, led to margins of victory for George Bushthat ranged from 225 to 493 votes and that the six others, including one pur-sued by George Bush, led to margins of victory for Al Gore that ranged from42 to 171 votes.)

9 The Branches of StatisticsTwo branches, descriptive statisticsand inferential Statistics , comprise the fieldof StatisticsCONCEPTThe branch of Statistics that focuses on collecting, summarizing,and presenting a set of data. EXAMPLESThe average age of citizens who voted for the winning candi-date in the last presidential election, the average length of all books aboutstatistics, the variation in the weight of 100 boxes of cereal selected from afactory s production are most likely to be familiar with this branch of sta-tistics, because many examples arise in everyday life.

10 Descriptive statisticsforms the basis for analysis and discussion in such diverse fields as securitiesCHAPTER 1 Fundamentals OF STATISTICS4 Categorical Variables Numerical Variables Examples Gender, a variable that has The number of previousthe categories male and elections in whicha citizen voted, a discreteAcademic major, a variable thatnumerical have the categories English, Math, Science, and The household income of aHistory, among others. citizen who voted, a continuousvariable. important point1J. Calmes and E. P.