Analytical Chem istry - DePauw University

84 Analytical Chemistry 2.0Table 4.11 Results for Two Determinations of the Mass ofa Circulating United States PennyFirst ExperimentSecond ExperimentPenny Mass (g) Penny Mass (g)1 3.080 1 3.0522 3.094 2 3.1413 3.107 3 3.0834 3.056 4 3.0835 3.112 5 3.0486 3.1747 3.198X 3.117 3.081s 0.051 0.037ing a small sample of pennies. We begin by making a distinction betweenpopulations and samples.4D.1 Populations and SamplesA population is the set of all objects in the system we are investigating. Forour experiment, the population is all United States pennies in circulation.This population is so large that we cannot analyze every member of thepopulation. Instead, we select and analyze a limited subset, or sample of thepopulation. The data in Table 4.11, for example, are results for two samplesdrawn from the larger population of all circulating United States pennies.4D.2 Probability Distributions for PopulationsTable 4.11 provides the mean and standard deviation for two samples ofcirculating United States pennies. What do these samples tell us about thepopulation of pennies? What is the largest possible mass for a penny? Whatis the smallest possible mass? Are all masses equally probable, or are somemasses more common?To answer these questions we need to know something about how themasses of individual pennies are distributed around the population’s averagemass. We represent the distribution of a population by plotting theprobability or frequency of obtaining an specific result as a function of thepossible results. Such plots are called probability distributions.There are many possible probability distributions. In fact, the probabilitydistribution can take any shape depending on the nature of the population.Fortunately many chemical systems display one of several commonprobability distributions. Two of these distributions, the binomial distributionand the normal distribution, are discussed in this section.