DATA SUMMARY AND DISPLAY in .NET Create QR in .NET DATA SUMMARY AND DISPLAY 6-1 DATA SUMMARY AND DISPLAYCompose qr code jis x 0510 on .netusing vs .net todraw qr codes with asp.net web,windows applicationx = 13VS .NET qr code jis x 0510 recognizer in .netUsing Barcode recognizer for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications.Figure 6-1 The sample mean as a balance point for a system of weights. .net Framework barcode decoder in .netUsing Barcode decoder for .net vs 2010 Control to read, scan read, scan image in .net vs 2010 applications.12 Pull-off force Attach barcode in .netusing vs .net crystal todraw barcode on asp.net web,windows applicationhypothetical population, because it does not physically exist. Sometimes there is an actual physical population, such as a lot of silicon wafers produced in a semiconductor factory. In previous chapters we have introduced the mean of a probability distribution, denoted . If we think of a probability distribution as a model for the population, one way to think of the mean is as the average of all the measurements in the population. For a nite population with N measurements, the mean isControl qr code size on .net c# qr size in visual c#a xi QR barcode library with .netusing asp.net web pages touse quick response code in asp.net web,windows application(6-2)Control quick response code size on vb qr bidimensional barcode size for vb.netThe 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.net Vs 2010 Crystal barcode integrated on .netusing .net crystal toinsert barcode for asp.net web,windows applicationi 1 n ANSI/AIM Code 39 creation with .netgenerate, create barcode 3 of 9 none in .net projectsx2 2 1 (6-3)Qrcode barcode library on .netuse visual studio .net crystal qr code jis x 0510 generator todraw qr code with .netThe sample standard deviation, s, is the positive square root of the sample variance. Make bar code with .netusing barcode integration for visual .net crystal control to generate, create barcode image in visual .net crystal applications.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.VS .NET Crystal upc e creator on .netusing .net vs 2010 crystal toinsert upc e on asp.net web,windows applicationCHAPTER 6 RANDOM SAMPLING AND DATA DESCRIPTION Deploy qrcode on .netusing barcode printer for aspx.cs page control to generate, create denso qr bar code image in aspx.cs page applications.x 12 x2 13 x8 14 15 Asp.net Website datamatrix drawer on .netuse aspx data matrix creation toattach ecc200 in .netx3 x6 x5 Control pdf417 2d barcode data for .net pdf-417 2d barcode data in .netFigure 6-2 How the sample variance measures variability through the deviations xi x. Include 2d matrix barcode with .netuse rdlc reports net matrix barcode integrating toconnect 2d matrix barcode for .netx7 x4 Control upca size on .net upc-a supplement 2 size with .netEXAMPLE 6-2Embed pdf-417 2d barcode with .netusing an asp.net form tomake pdf417 2d barcode on asp.net web,windows applicationTable 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 1xiEuropean Article Number 13 barcode library in .netusing barcode generating for rdlc reports control to generate, create ean13 image in rdlc reports applications.i 1 8Control pdf-417 2d barcode size on javato display pdf 417 and pdf417 data, size, image with java barcode sdkx2 2so the sample variance is s2 1.60 8 1 1.60 7 0.2286 1pounds2 2 and the sample standard deviation is s 0.48 pounds 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 ensureTable 6-1 Calculation of Terms for the Sample Variance and Sample Standard Deviation i 1 2 3 4 5 6 7 812.6 12.9 13.4 12.3 13.6 13.5 12.6 13.1 104.00.4 0.1 0.4 0.7 0.6 0.5 0.4 0.1 0.0x2 20.16 0.01 0.16 0.49 0.36 0.25 0.16 0.01 1.606-1 DATA SUMMARY AND DISPLAY numerical accuracy. A more ef cient computational formula for the sample variance is obtained as follows: a 1xii 1 n x2 2 1s2 and since x a 1xi x2 n 1 2xxi 2 a xi nx2 n 1 2x a xi n 11 n2 g i xi, this last equation reduces to a xi s2 a a xi b n n 1 (6-4)Note that Equation 6-4 requires squaring each individual xi, then squaring the sum of the xi, subtracting 1 g xi 2 2 n from g x2, and nally dividing by n 1. Sometimes this is called the i shortcut method for calculating s2 (or s). EXAMPLE 6-3 We will calculate the sample variance and standard deviation using the shortcut method, Equation 6-4. The formula givesn 2 a xi a a xi b s2 and n n 1 1353.6 10.2286 711042 2 81.60 7