Absolute deviation

Model Chemistry MAD Standard Deviation Absolute Max. Error... 

Correlation Average Deviation Absolute Average Deviation Bias Maximum Deviation... 

The precisions were found to be similar and the pooled standard deviation (absolute) computed to be 0.071%. Comment upon the efficiency of the mixing. 

Year Reported Sample Type Number of Results Standard Deviation (% Absolute)... 

Correlation Absolute average deviation, % Absolute average deviation, Btu/lb Absolute average deviation, %... 

For each combination of atoms i.j, k, and I, c is defined by Eq. (29), where X , y,. and Zj are the coordinates of atom j in Cartesian space defined in such a way that atom i is at position (0, 0, 0), atomj lies on the positive side of the x-axis, and atom k lies on the xy-plaiic and has a positive y-coordinate. On the right-hand side of Eq. (29), the numerator represents the volume of a rectangular prism with edges % , y ., and Zi, while the denominator is proportional to the surface of the same solid. If X . y ., or 2 has a very small absolute value, the set of four atoms is deviating only slightly from an achiral situation. This is reflected in c, which would then take a small absolute value the value of c is conformation-dependent because it is a function of the 3D atomic coordinates. 

Another measure of dispersion is the coefficient of variation, which is merely the standard deviation expressed as a fraction of the arithmetic mean, viz., s/x. It is useful mainly to show whether the relative or the absolute spread of values is constant as the values are changed. 

Standard Deviation The absolute standard deviation, s, describes the spread of individual measurements about the mean and is given as... 

The variance is just the square of the absolute standard deviation. Using the standard deviation found in Example 4.3 gives the variance as... 

Determine the density at least five times, (a) Report the mean, the standard deviation, and the 95% confidence interval for your results, (b) Eind the accepted value for the density of your metal, and determine the absolute and relative error for your experimentally determined density, (c) Use the propagation of uncertainty to determine the uncertainty for your chosen method. Are the results of this calculation consistent with your experimental results ff not, suggest some possible reasons for this disagreement. 

Determine Ks and the amount of sample needed to give a relative standard deviation for sampling of 2.0%. Predict the percent relative standard deviation and the absolute standard deviation if samples of 5 g are collected. 

To determine Ks we need to know the average mass of the cereal samples and the relative standard deviation for the %(w/w) ash. The average mass of the five cereal samples is 1.0007 g. The average %(w/w) ash and the absolute standard deviation are, respectively, 1.298% and 0.03194. The percent relative standard deviation, therefore, is... 

The bond orders in the polymethine chain are equalized in the ground and excited states. If Tg = 45°, the bond equalization is maximum. This is the ideal polymethine state (1) of the polymethine chain. Any deviation from this state (ie, Oq is greater than or less than 45°) causes the bond to alternate from the polymethine chain center to its ends. The alternation ampHtude is found to be proportional to the absolute value 45° — 4>g. ... 

Defubed as the average absolute deviation of the four traction values from the mean. The range is determined by the type and condition of grass. ... 

Correlations based on reference substances are limited to compounds which have experimentally determined values, but the number of data points needed to produce a correlation is relatively small. A reference substance should be as chemically and physically compatible to the chemical with which it is being compared as possible. Use of reference substances in the ideal assumes no property deviations, thus the smaller the deviations, the lower the absolute error in the correlations. 

Values for 32 elements and the constant have been tabulated (159). An average absolute error of 9.6% for 721 soHd compounds (13% standard deviation) and 8.8% for 477 Hquid compounds (11.5% standard deviation) has been reported. 

Lee and Thodos expanded their earlier treatment of self-diffusivity to cover 58 substances and 975 data points, with an average absolute deviation of 5.26 percent. Their correlation is too involved to repeat here, but those interested should refer to the original paper. 

Umesi-Danner They developed an equation for nonaqueous solvents with nonpolar and polar solutes. In all, 258 points were involved in the regression. Rj is the radius of gyration in A of the component molecule, which has been tabulated by Passut and Danner for 250 compounds. The average absolute deviation was 16 percent, compared with 26 percent for the Wilke-Chang equation. 

Siddiqi-Lucas In an impressive empirical study, these authors examined 1275 organic liquid mixtures. Their equation yielded an average absolute deviation of 13.1 percent, which was less than that for the Wilke-Chang equation (17.8 percent). Note that this correlation does not encompass aqueous solutions those were examined and a separate correlation was proposed, which is discussed later. 

Siddiqi-Lucas These authors examined 658 aqueous liqiiid mixtures in an empirical study. They found an average absolute deviation of 19.7 percent. In contrast, the Wilke-Chang equation gave 35.0 percent and the Hayduk-Laudie correlation gave 30.4 percent. 

Riazi-Whitson They presented a generahzed correlation in terms of viscosity and molar density that was apphcable to both gases and liqmds. The average absolute deviation for gases was only about 8 percent, while for liquids it was 15 percent. Their expression relies on the Chapman-Enskog correlation [Eq. (5-194)] for the low-pressure diffusivity and the Stiel-Thodos correlation for low-pressure viscosity ... 

Vigne.s empirically correlated mixture diffusivity data for 12 binary mixtures. Later Ertl et al. evaluated 122 binary systems, which showed an average absolute deviation of only 7 percent. None of the latter systems, however, was veiy nonideal. 

Siddiqi-Lucas suggested that component volume fractions might be used to correlate the effects of concentration dependence. They found an average absolute deviation of 4.5 percent for nonpolar-nonpolar mixtures, 16.5 percent for polar-nonpolar mixtures, and 10.8 percent for polar-polar mixtures. 

One particular case of multicomponent diffusion that has been examined is the dilute diffusion of a solute in a homogeneous mixture (e.g., of A in B -h C). Umesi and Danner compared the three equations given below for 49 ternaiy systems. All three equations were equivalent, giving average absolute deviations of 25 percent. 

Based on 23 data points for 3 systems. Average absolute deviation 26%. Use with surface area of drop after detachment occurs, = velocity through nozzle <3 = iuterfacial tension. 

E] Average absolute deviation 11% for 20 data points for 3 systems. 

Stainless steel flat six-blade turbine. Tank had four baffles. Correlation recommended for ( ) < 0.06 [Ref. 156] a = 6( )/<, where d p is Sauter mean diameter when 33% mass transfer has occurred. dp = particle or drop diameter <3 = iuterfacial tension, N/m ( )= volume fraction dispersed phase a = iuterfacial volume, 1/m and k OiDf implies rigid drops. Negligible drop coalescence. Average absolute deviation—19.71%. Graphical comparison given by Ref. 153. ... 

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