Applied Statistics Statistica

Statistical techniques are primarily used to manage data. For example, statistics might try to make sound generalizations about the characteristics of a given population. Rather than analyze the entire group, however, such conclusions are typically drawn from more manageable population samples. In order for the generalizations to be valid, these samples must be random.

Random sampling can be defined as "a method of selecting a sample in such a way that every possible sample has the same probability of being selected." Populations may be either finite or infinite. Finite populations consist of a fixed number of elements; whereas, infinite populations have a limitless number of values. With finite populations, random samples can be determined through the use of random numbers. Such numbers may be either obtained from tables or generated by computer. Items within a population can then be selected from numbered lists. With infinite populations, a sample is considered random if it has a corresponding distribution of independent random variables. This ensures that the sample represents the particular infinite population's overall characteristics.

Most any survey or poll will employ some form of random sampling. As an example, the popularity of television programs is based on "ratings." These ratings--which are based on a random sample of viewers--may then be used to make programming decisions. Recently, as a result of low r

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d mean is a more sophisticated form of the arithmetic mean. In any group of data, there are sometimes certain values that are more important than others. When averaging such groups, it is sometimes necessary to assign increased significance to such values. The mathematical technique for creating a weighted average involves various steps. First, weights must be assigned to each value based on its relative importance. Only then can the weighted mean be calculated. For example, the weighted mean, xw, of a set of numbers x1, x2, x3, . . . xn, whose relative importance is expressed numerically by a corresponding set of numbers w1, w2, w3, . . . wn, may be given by the following formula: xw = w1x1 + w2x2 + . . . wnxn = S w(x w1 + w2 + . . . wn S w In this equation, S w(x may be defined as the "sum of the products obtained by multiplying each x by the corresponding weight" and S w is the "sum of the weights." Perhaps the most widely used and quoted weighted average is the Dow Jones industrial average. This financial average is comprised of 30 of the biggest and best-known American stocks. Each stock's contribution is weighted according to its per-share closing price. Thus, in 1994, when th
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Approximate Word count = 2549
Approximate Pages = 10 (250 words per page)

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