Mean average

To extend the applicability of the characterization factor to the complex mixtures of hydrocarbons found in petroleum fractions, it was necessary to introduce the concept of a mean average boiling point temperature to a petroleum cut. This is calculated from the distillation curves, either ASTM or TBP. The volume average boiling point (VABP) is derived from the cut point temperatures for 10, 20, 50, 80 or 90% for the sample in question. In the above formula, VABP replaces the boiling point for the pure component. 

The measurement techniques most frequently used are derived from Raoult s and Van t Hoff s laws applied to cryometry, ebulliometry, osmometry, etc. They are not very accurate with errors on the order of ten per cent. Consequently, the molecular weight is often replaced by correlated properties. The mean average temperature or viscosity can thus replace molecular weight in methods derived from ndM. 

For undefined hydrocarbon mixtures, the liquid density may be predicted at any temperature (T) from the mean average boiling point (MeABP) and the specific gravity (sp gr) by Eq. (2-94), adopted from Ritter et al. ... 

Properties are evaluated at the length mean average temperature. 

However, for many cases, particularly when the difference in specific volume is large, the log mean average is much better. 

Devarda s alloy 303, 679 Deviation mean (average), 134 standard, 134... 

Mean absolute deviation MAD is a statistical measure of the mean (average) difference between a product s forecast and actual usage (demand). The deviations (differences) are included without regard to whether the forecast was higher than actual or lower. 

The impact operator corrected in such a way still remains semiclassical though the requirements of detailed balance are satisfied. It is reasonable provided that the change of rotational energy is small on average, relative to translational energy ey — ej < ikT, where the overbar means averaging performed over the distribution of products after collision. 

First, we define a mean (average) size of particles in the distribution as d, and then define what we call a "standard deviation as a, for the distribution of particles. From statistics, we know that this means that 68% of the particles are being counted (34% on either side of the mean, d), i.e. -... 

A dissimilarity plot is then obtained by plotting the dissimilarity values, dj, as a function of the retention time i. Initially, each p 2 matrix Y, consists of two columns the reference spectrum, which is the mean (average) spectram (normalised to unit length) of matrix X, and the spectrum at the /th retention time. The spectrum with the highest dissimilarity value is the least correlated with the mean spectrum, and it is the first spectrum selected, x, . Then, the mean spectrum is replaced by x, as reference in matrices Y, (Y, = [x j x,]), and a second dissimilarity plot is obtained by applying eq. (34.14). The spectrum most dissimilar with x, is selected (x 2) and added to matrix Y,-. Therefore, for the determination of the third dissimilarity plot Y, contains three columns [x, x 2 /]> wo reference spectra and the spectmm at the /th retention time. 

The overbar means average. The k in the proportionality constant is called the Boltzmann constant. It is equal to R, the gas constant, divided by Avogadro s number. Note that k is the same for all gases. 

Minimum Median mean average Maximum Observations... 

The analytical results for each sample can again be pooled into a table of precision and accuracy estimates for all values reported for any individual sample. The pooled results for Tables 34-7 and 34-8 are calculated using equations 34-1 and 34-2 where precision is the root mean square deviation of all replicate analyses for any particular sample, and where accuracy is determined as the root mean square deviation between individual results and the Grand Mean of all the individual sample results (Table 34-7) or as the root mean square deviation between individual results and the True (Spiked) value for all the individual sample results (Table 34-8). The use of spiked samples allows a better comparison of precision to accuracy, as the spiked samples include the effects of systematic errors, whereas use of the Grand Mean averages the systematic errors across methods and shifts the apparent true value to include the systematic error. Table 34-8 yields a better estimate of the true precision and accuracy for the methods tested. 

If a large number of readings of the same quantity are taken, then the mean (average) value is likely to be close to the true value if there is no systematic bias (i.e., no systematic errors). Clearly, if we repeat a particular measurement several times, the random error associated with each measurement will mean that the value is sometimes above and sometimes below the true result, in a random way. Thus, these errors will cancel out, and the average or mean value should be a better estimate of the true value than is any single result. However, we still need to know how good an estimate our mean value is of the true result. Statistical methods lead to the concept of standard error (or standard deviation) around the mean value. 

The procedure used to determine whether a given result is unacceptable involves running a series of identical tests on the same sample, using the same instrument or other piece of equipment, over and over. In such a scenario, the indeterminate errors manifest themselves in values that deviate, positively and negatively, from the mean (average) of all the values obtained. Given this brief background, let us proceed to define some terms related to elementary statistics. 

Fig. 9. Maximum Lyapunov exponents along the orbits in the space phase for scale maximum Sm = 1-5 (compare with Figure 8). Even for experiment E2.b (which has the smallest attractor) the maximum Lyapunov exponent holds positive. The average values of the Lyapunov exponents where computed by neglecting the transitory effects (AVWT means Average Value without Transitory effects).

C20 APD95 = concentration of drug which caused a 20% increase in action potential duration at 95% repolarization (APD95). Reported is the log mean average of n determinations with the lowest and highest values given in parentheses. 

MEASUREMENTS OF THE CRUSHING STRENGTH OF A TABLET FORMULATION, jc, = a-LACTOSE 2= p-LACTOSE Xj = RICE STARCH Y-MEAN = AVERAGE OF TEN MEASUREMENTS OF THE CRUSHING STRENGTH (N)... 

The actual falling weight of a steam hammer is 1200 pounds, the cylinder is 10 inches in diameter, and the stroke is 27 in. The mean average steam pressure is 80 psi. (a) What is the energy of the hammer blow (b) What is the average force exerted by the hammer if it travels 1/8 in. after striking the workpiece ... 

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