Mean values calculation

The microcanonical ensemble is a certain model for the repetition of experiments in every repetition, the system has exactly the same energy, Wand F but otherwise there is no experimental control over its microstate. Because the microcanonical ensemble distribution depends only on the total energy, which is a constant of motion, it is time independent and mean values calculated with it are also time independent. This is as it should be for an equilibrium system. Besides the ensemble average value (il), another coimnonly used average is the most probable value, which is the value of tS(p, q) that is possessed by the largest number of systems in the ensemble. The ensemble average and the most probable value are nearly equal if the mean square fluctuation is small, i.e. if... 

Sixteen freely programmable computational formulae with assignment of the calculation parameters and units, mean-value calculations and arithmetic of one titration to another (via common variables) are available. Results can be calculated without any limitations. 

Mean value calculated from the trans- and -configurations. 

Fig. 8. Avoidance behavior towards an unprotected area displayed by the offspring of mice treated with the mutagen ethyl-nitrosourea (ENU). The behavior of the offspring is compared to a mean value calculated from the genetic background strain. Mice differing more than 2.75 SDs from the mean value (indicated by circles) are considered to be potential mutants and, after confirmation of the phenotype, are selected as founders for a ENU-mutant line...

Cells that have migrated are counted in at least 10 high powered fields (x400) using a standard microscope, and the mean value calculated. 

Mean value calculated from double determinations of element concentrations > 10 LoD. 

The mean value of all the series is 0 089897, but Morley considered the results of the first and second series to be too high, owing to the presence of mercury-vapour in the glass globe. This source of error was eliminated in the other three series, the mean value calculated from them being 0 089873 0 0000027 gram. 

In a "dying acid" type of experiment with no additions/with-drawals, the fresh acid replacement rate has no real meaning. Values calculated for the mixer comparison data are called equivalent replacement rates. These equivalent replacement rates are the rates necessary (i.e., for a given diluent formation rate) to maintain equilibrium in a hypothetical steady state alkylation unit which uses fresh acid at 98% titratable acidity and spends its acid at the acid strength in question. 

The introduction of the formulation of the statistical hypotheses and their checking have already been presented in Section 5.2.2.1 where we proposed the analysis of the comparison between the mean values and dispersions of two selections drawn from the same population. If we consider the mean values in our actual example, the problem can be formulated as follows if xi is the mean value calculated with the values in Table 5.4 and X2 is the mean value for another selection extracted from the same population (such as for example X2, which is the limiting reactant concentration at the reactor input for Table 5.2, column 2) we must demonstrate whether Xj is significantly different from X2-A similar formulation can be established in the case of two different dispersions in two selections extracted from the same population. Therefore, this problem can also be extended to the case of two populations with a similar behaviour, even though, in this case, we have to verify the equality or difference between the mean values pj and P2 ot between the variances and Oj. We frequently use three major computing steps to resolve this problem and to check its hypotheses ... 

Faces. No. of Measurements. Angle Limits. Mean Value. Calculate tl Value. 

FIGURE 9.7 Anomalies of the yearly and seasonal mean temperatures of the entire Baltic Sea with regards to the mean values calculated for the period 1990-2005 (a) mean, (h) spring, (c) summer, (d) autumn, (e) winter. 

If mean values calculated for the whole water column are compared, especially if the water depth is highly variable between the stations and the number of samples taken from various water layers is different, care must be taken with the interpretation of the results. For instance, mean concentrations of particulate organic matter (POM) calculated for all depths show a gradient (Fig. 12.12) with higher concentrations in the shallow western areas of the... 

The data in Fig. 6 are described according to how it is to be plotted. Values and processed data from two tests with different operators are indicated. Column 1 shows the four Cm controls, the mean value calculated from these four controls in any single plate, and the SD of the data. The second column shows the data from a test involving a single plate. The mean value (0.78) and the SD (0.03) are put into relevant boxes after their calculation. These are plotted on the DDD charts (gray shaded boxes). The date and operator are added. The SDC value is calculated for the sum of all the mean values on all plates in a given test (in this case 1 plate so that SDC data are identical to the DDD data). 

Eatough et al. (1989b) report individual data from 20 indoor environments including homes, businesses, and discos. Mean values calculated from these data are 3-ethenylpyridine (3.2pg/m ) 2-ethenylpyridine (0.3pg/m ) pyridine (2.5pg/m ) myosmine (0.4pg/m ) and cotinine (0.3pg/m ). The corresponding nicotine mean is 14.8pg/m. ... 

F irst and second figures are for, respectively, adult and larval spot shrimp 10 h exposure mean values calculated from T able 2 of reference for exposure of adults to pH]- or p C] naphthalene naphthyl glucuronide and a part of the dihydrodiol component may be impurities, j May not include quinones. 

Here, the value 0.73 was used for the partial specific volume, v, and 0.53 gram of water per gram of protein as the hydration value, w. These are mean values calculated from an earlier study of the hydrodynamic properties of 21 globular proteins of known structure (ref. 74). Calibration constants in terms of molecular radii (r and r. ), given in Table 1, provide an estimate of the limiting values of these parameters for separation by the primary SEC process on the TSK-SW columns used. 

Mean value calculated from amide A and I bands, No IR data, film loo thick. 

By combination of such moments one can easily calculate mean values for the degree of polymerization, P, which characterize the chain length distribution. The distribution is only fully described if all moments are known. However, in practice there are two mean values calculated by the first three statistical moments, which are extensively used the number-average degree of polymerization, P, and the weight-average degree of polymerization,... 

The H/L ratios were calculated separately for each sample and the mean values calculated from all the individual measurements are given in the table. 

Only data resulting from comparable measurements should be used to calculate the mean value. In general, the mean value should be based on at least three individual measurements. Significantly smaller or larger measured values must not be omitted, unless they are proved to be outliers. This strict rule can be softened if the measurements are carried out in one and the same laboratory. In this case, one deviating measured value can be replaced by three others. Mean value calculation is not allowed if the timely sorted measured values exhibit upward or downward trends. 

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