Standard Deviation SD

SD of a data set is a measure of how spread out the data is it is the average distance from the mean of the data set to a point, calculated by the sum of squares of the distances from each data point to the mean of the set divided by a subset of the population, expressed as n - 1  

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Statistically, the standard deviation (SD) from the mean Is given by the formula,... 

In this case the differences (d) between each pair of results are calculated and S, the mean of the difference, is obtained. The standard deviation sd of the differences is then evaluated. The results are tabulated as follows. 

One drag level (Cindiv) can be used with the means and standard deviation (SD) of population parameters (Ppop) as a priori knowledge for an individual parameter estimate using the Bayesian objective function. 

If, despite the fact that the x and the y values are paired, a Mest was applied to the difference (Xmean ymean) using the standard deviations Sd = 0.0583 according to Eq. (1.18), a r-value of 2.16 would be found, which is smaller than the critical tc(2n 2) = 2.306. The two series thus could not be distinguished. The overall mean, found as 1.63, would be advanced. 

In children, the diagnosis of GH deficiency is further supported if height is more than two standard deviations (SD) below the population mean (age- and sex-matched).35 Failure of linear growth is an almost universal presenting feature of childhood GH deficiency. 

Compound Identification Number IC50 (pM) Standard Error (SE) of Fit or Standard Deviation (SD) from Multiple, Independent Determinations Hill Coefficient Maximum % Inhibition Attained Comments... 

Four neutral lipid models were explored at pH 7.4 (1) 2% wt/vol DOPC in dode-cane, (2) olive oil, (3) octanol, and (4) dodecane. Table 7.5 lists the effective permeabilities Pe, standard deviations (SDs), and membrane retentions of the 32 probe molecules (Table 7.4). The units of Pe and SD are 10 6 cm/s. Retentions are expressed as mole percentages. Figure 7.22a is a plot of log Pe versus log Kd (octanol-water apparent partition coefficients, pH 7.4) for filters loaded with 2% wt/vol DOPC in dodecane (model 1.0, hlled-circle symbols) and with phospholipid-free dodecane (model 4.0, open-circle symbols). The dashed line in the plot was calculated assuming a UWL permeability (see Section 7.7.6) Pu, 16 x 10-6 cm/s (a typical value in an unstirred 96-well microtiter plate assay), and Pe of 0.8 x 10-6 cm/s... 

It can be shown that the standard deviation (SD) of this distribution is also just yfji. In other words, if one would repeatedly measure the same pixel that on average collects 100 photons during a single dwell time (a normal value for a rather bright confocal image ) one would record less than 100-2x /l00 = 80 photons or more than 100 + 2x /l00 = 120 photons just by coincidence in 5% of the measurements. This uncertainty is expressed as the... 

Table 4.56. Statistical means and standard deviations (SD) for bond dissociation energies (BDEs) o/ M—H and M—Me bonds of saturated MH X (X = H, Me) transition-metal complexes from the first three series of the d block...

The log deviation are logC<0.1, standard deviation (SD) is between 5% 30%. (majority element s standard deviation less than 10%, only that of S and Os are less than 30%)... 

Lead(II) adsorbed on both columns was quantitatively eluted with ca. 6 bed volumes of 1 M nitric acid. In this work, 2 cylcles of the adsorption-elution operation were repeated at each flow rate. Then 16 cycles of the adsorption and elution operation were conducted for each column. In the case of FPS-f column, averaged recovery was 104% with standard deviation (sd) of 4 % (n = 16) and for the other column, averaged recovery 103% with sd of 4 %. Table 3 summarizes numerical data for results shown in Fig. 4. Breakthrough capacities at C/Co = 0.05 are 0.54 - 0.57 and 0.28 - 0.33 mmol/g for FPS-f and FP columns, respectively. Total uptake was 0.78 -0.83 mmol/g for FPS-f and 0.51 - 0.54 mmol/g for RF-f. During repeated adsorption-elution operations, no deterioration of both RFP-f and FP-f was observed. 

FIGURE 4.2. Setting thresholds using historical control data. The figure shows a Gaussian ( normal ) distribution of screen parameters 99.7% of the observations in the population are within three standard deviations (SD) of the historic mean. Here the threshold (i.e., the point at which a datum is outside of normal ) was set at Xc = mean + 3 SD. Note that such a screen is one-sided. 

Limitations on our ability to measure constrain the extent to which the real-world situation approaches the theoretical, but many of the variables studied in toxicology are in fact continuous. Examples of these are lengths, weights, concentrations, temperatures, periods of time, and percentages. For these continuous variables, we may describe the character of a sample with measures of central tendency and dispersion that we are most familiar with the mean, denoted by the symbol x and also called the arithmetic average, and the standard deviation SD, denoted by the symbol [Pg.870]

Most commonly, location is described by giving the (arithmetic) mean and dispersion by giving the standard deviation (SD) or the standard error of the mean (SEM). The calculation of the first two of these has already been described. If we again denote the total number of data in a group as N, then the SEM would be calculated as... 

The standard deviation (SD) and the standard error of the mean (SEM) are related to each other but yet are quite different. 

Obstacles of ionisation interferences in the quantitative determination of the N-containing surfactants from industrial blends dissolved together with AE compounds in methanol applying FIA-MS can be minimised or even eliminated if quantification was performed in the standard addition mode. So the standard deviations (SD) observed now reached a maximum of 7% for N-containing compounds whereas AE could be quantified with a SD of 4%. In parallel, the time investment for FIA-MS quantification in the standard addition mode, however, increased considerably and reached a factor of 3-4. 

Nominal LC50 values and standard deviation (SD) after 24 h of exposure to different LAS homologues and commercial LAS for seabream eggs and larvae, as well as ratio between LC50 (eggs) and LC50 (larvae)... 

Solvent CAS No. Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Mean Standard Deviation % SD... 

TABLE 4. Heats of formation and standard deviations (SD) (kcalmol ) for amino compounds as calculated by the MM2 and MM3 force fields and observed by experiment0 . Reprinted with permission from Refs. 5 and 6. Copyright (1985, 1990) American Chemical Society... 

Validation of methods for quantitative determination of impurities includes precision studies. Repeatability is generally assessed by analysis of the same sample or samples prepared by the same analyst in replicate assays within a short duration of time. Repeatability should be assessed using (i) a minimum of nine determinations covering the specified range for the procedure (e.g., three concentrations/three replicates each) or (ii) a minimum of six determinations at 100% of the test concentration. Repeatability is evaluated by averaging the mean results from replicate assays and calculating the standard deviation (SD) and RSD. Repeatability of the method can be stated as either SD or RSD values. If an instrument is required for assay performance, then the same instrument should be used for the replicate assays. 

Mean particle size (ECD) (nm) Standard deviation (SD)(nm) Mean particle size (ECD) (nm) Standard deviation (SD)(nm)... 

Figure 8.15 (A-F) hiistogram representations of the PLS score images showing the statistical distributions of the API class. Heterogeneity In the blend Is Indicated by deviations from a normal distribution and can be expressed as percent standard deviation (%SD), calculated by dividing the standard deviation by the mean.

STL s quality-control programme includes the recovery of known additions of analyte, analysis of externally supplied standards, calibration, analysis of duplicates and control charting. Each analyte is monitored by analysing at least one AQC standard for every 20 samples. AQC results are plotted on control charts and action is taken if a point Hes outside +3 standard deviations (SD) or if two consecutive points He outside +2 SDs. 

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