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The sample mean, x, is a reasonable estimate of the population mean, . Therefore, the engineer designing the connector using a 3 32-inch wall thickness would conclude, on the basis of the data, that an estimate of the mean pull-off force is 13.0 pounds. Although the sample mean is useful, it does not convey all of the information about a sample of data. The variability or scatter in the data may be described by the sample variance or the sample standard deviation. De nition If x1, x2, p , xn is a sample of n observations, the sample variance is a 1xi

x2 2 1 (6-3)

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The units of measurements for the sample variance are the square of the original units of the variable. Thus, if x is measured in pounds, the units for the sample variance are (pounds)2. The standard deviation has the desirable property of measuring variability in the original units of the variable of interest, x. How Does the Sample Variance Measure Variability To see how the sample variance measures dispersion or variability, refer to Fig. 6-2, which shows the deviations xi x for the connector pull-off force data. The greater the amount of variability in the pull-off force data, the larger in absolute magnitude some of the deviations xi x will be. Since the deviations xi x always sum to zero, we must use a measure of variability that changes the negative deviations to nonnegative quantities. Squaring the deviations is the approach used in the sample variance. Consequently, if s2 is small, there is relatively little variability in the data, but if s2 is large, the variability is relatively large.

EXAMPLE 6-2

Complex software systems usually involve many applications communicating with each other and with databases. In the past, deploying large software systems required copying files to the destination location, because the COM components required Registry entries to operate. It s not always possible to jump over to the .NET Framework, abandoning the hundreds of COM components that have been developed over the past several years. A phased approach can limit the risk involved. Migrating to the .NET Framework usually means that a development team must decide which COM components will be migrated to .NET and which COM components will be used with COM interoperability. This comes with its own set of challenges. The first part of this chapter explores some methods for migrating from ASP code to ASP.NET. Later, chapter examines early and late binding techniques for using COM components. Finally, the chapter covers some methods for deploying ASP.NET Web applications.

Table 6-1 displays the quantities needed for calculating the sample variance and sample standard deviation for the pull-off force data. These data are plotted in Fig. 6-2. The numerator of s2 is a 1xi

i 1 8

17

x2 2

Computation of s2 The computation of s2 requires calculation of x, n subtractions, and n squaring and adding operations. If the original observations or the deviations xi x are not integers, the deviations xi x may be tedious to work with, and several decimals may have to be carried to ensure

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Table 6-1 Calculation of Terms for the Sample Variance and Sample Standard Deviation i 1 2 3 4 5 6 7 8

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