Tabulating numbers

Basically, the tabled values represent area (proportions or probability) associated with a scaling variable designated by Z in Fig. 3-56. The normal cui ve is centered at 0, and for particular values of Z, designated as z, the tabulated numbers represent the corresponding area under the cui ve between 0 and z. For example, between 0 and 1 the area is. 3413. (Get this number from Table 3-4. The value of A includes the area on both sides of zero. Thus we want A/2. For z = 1, A = 0.6827, A/2 = 0.3413. For z = 2, A/2 = 0.4772.) The area between... 

Estimate (or use actual tabulation) number of fittings, valves, etc. in system. Convert these to equivalent straight pipe using Figures 2-20 or 2-21, L g, or head by Figures 2-12 through 2-16 and Table 2-2. 

A numerical example may help. There are two crops, A and B, and two possible states of the weather. Good and Bad, assumed to be equally likely. The income from the crops under the two conditions are given in the following tabulation. Numbers in parentheses indicate the utility a fanner derives from the various income levels. They arc chosen to reflect the nearly... 

It is commonly believed that anyone who tabulates numbers is a statistician. This is like believing that anyone who owns a scalpel is a surgeon. 

The value of f is compared with tabular values, which are listed according to the number of degrees of freedom associated with the residual sum of squares and for various significance levels. If the computed value is larger than the tabulated number then the coefficient can be considered significant. 

The total of the numbers in the third column, in this case 3, is the test statistic. Table A. 12 is used for the Mann-Whitney [7-test again the critical values leading to the rejection of the null hypothesis are those which are less than or equal to the tabulated numbers. The table shows that for a one-sided test at P = 0.05, with five measurements of each sample, the test statistic must be <4 if the null hypothesis is to be rejected. In our example we can thus reject Hq the treatment of the silver-containing material probably does reduce the level of the metal. 

Simple discretization schemes use derivatives of Lagrangian interpolation polynomials that approximate the function known only at the grid points x,. These schemes consist of tabulated numbers multiplied by the function s values at m contiguous grid points and are referred to as "m-point-formulae" by Bickley [498] (cf. Ref. [468, p.914]). For an acceptable truncation error 0(h ), f = 4 or higher, m is larger than t which leads to an extended amount of computation. 

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