Statistics and Probability shorte Tarable sales Sikken by Industry 3rd Quarter 2011 features SENSEN Utilities 54 King and OEitection Intertainment Pie charts like the one this businessman is using are one common way to display statistics AP Images 10
STATISTICAL DATA 580 065 struction 213 592 294 Manufacturing 319 988 067 opinion polls in cost of living indexes and in reports of business trends and cycles Every science depends to some extent upon the gathering of data and the inter preting of the data by statistical methods On the basis of statistics I important decisions are made in the fields of government industry and education Even the average person bases many personal deci sions on information that has been supplied by statisticians The results of statistical inves tigations may sometimes be stated in a single sentence as in weather forecasting Often however they are presented in the form of numer ical tables or are shown pictorially in the form of graphs or charts HOW STATISTICAL DATA ARE COLLECTED Statistical data are usually collected in one of the following ways W by consulting existing source material such as 11
Statistics and Probability periodicals and newspapers or reports from industries government agencies and research bureaus 2 by setting up a survey and col lecting data thirsthand from individuals or organizations and 3 by conducting scientific experiments and measuring or counting under controlled conditions Basic information must be collected in such a way that it is accurate representative and as comprehensive as possible Statistical treatment cannot in any way improve the basic validity or accuracy of the raw data Methods of collecting data are therefore basic to the whole field of statistics POPULATIONS The term population ordinarily means the whole number of people in a specific place The stat istician speaks of a population of automobiles salaries accidents ballots blood pressures or any other characteristic For the statistician a population also called a universe means the entire group of items in the class being considered Usually it is not possible to gather observa tions from all the possible cases in a population Some populations are infinite For example 12
STATISTICAL DATA THE LAW OF LARGE NUMBERS In statistics the law of large numbers is the theorem that as the number of identically distributed randomly generated variables increases their sample mean aver age approaches their theoretical mean The theorem was first proved by the Swiss mathema tician Jakob Bernoulli in 1713 He and his contemporaries were developing a formal probability theory with a view toward analyzing games of chance Bernoulli envis aged an endless sequence of repetitions of a game of pure chance with only two outcomes a win or a loss Labeling the probability of a win p Bernoulli considered the fraction of times that such a game would be won in a large number of repetitions It was commonly believed that this fraction should eventually be close to p This is what Bernoulli proved in a precise manner by showing that as the number of repetitions increases indefinitely the probability of this fraction being within any pre specified distance from p approaches 1 if you should want to count how many times heads will turn up when a penny is tossed you would have to set a limit to the number of throws because even a billion would not exhaust the infinite universe of possible trials 13
