Percent relative standard deviation

The percent relative standard deviation is obtained by multiplying Sr by 100%. 

What are the standard deviation, the relative standard deviation, and the percent relative standard deviation for the data in Table 4.1 ... 

The relative standard deviation and percent relative standard deviation are... 

Few populations, however, meet the conditions for a true binomial distribution. Real populations normally contain more than two types of particles, with the analyte present at several levels of concentration. Nevertheless, many well-mixed populations, in which the population s composition is homogeneous on the scale at which we sample, approximate binomial sampling statistics. Under these conditions the following relationship between the mass of a randomly collected grab sample, m, and the percent relative standard deviation for sampling, R, is often valid. ... 

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... 

If we use 5.00-g samples, then the expected percent relative standard deviation is... 

Each of the f2 samples had a nominal weight of O.f g. Determine the approximate value for fQ, and the mass of sample needed to achieve a percent relative standard deviation of 2%. 

What mass of carbon is needed to give a percent relative standard deviation of 1.0% for the activity of a sample if counting is limited to 1 h How long must the radioactive decay from a 0.50-g sample of carbon be monitored to give a percent relative standard deviation of 1 % for the activity ... 

Thus, we expect that approximately 67% of the participants in the collaborative study (+I0) will report the analyte s concentration within the range of 98% w/w to 102% w/w. When the analyte s concentration is 0.1% w/w (C = 0.001), the estimated percent relative standard deviation is... 

Of course, equation 14.26 only provides an estimate of the variability in results submitted by those participating in a collaborative study. A relative standard deviation that is within one-half to twice the estimated value suggests that the method performs acceptably when used by analysts in different laboratories. The percent relative standard deviation for a single analyst should be one-half to two-thirds that for the variability between analysts. 

The minimum number of sample increments required can be calculated from either Equation 2 or 5. From Equation 2, assuming that a 50% level of confidence is desired and that an acceptable percent relative standard deviation R is 50, n... 

The % corrected peak area values are shown in Table 2. When an injection time of 20 to 40 sec is used, the assay generated reasonable precision. The overall percent relative standard deviation (%RSD) are 0.7, 1.6, and 7.6 for the HC, LC, and non-main species, respectively. The %RSD of HMW species is relatively high due to poor resolution between the HMW and HC peaks. In this case, we recommend that the HMW species not be integrated separately from the HC component unless there is a clear graphic valley point for integration. 

As a further means of comparing the datasets produced by the two techniques, group means, standard deviation from mean, and percent relative standard deviation from mean were calculated for each measured element as a way of quantifying the amount of dispersion present in each analytical group (Table Ila and b). 

Table 10.3 shows a reduction in the percent relative standard deviation (%RSD) by a factor of two for 10 replicate injections. 

When the various instrumental and chromatographic factors are set for optimum performance, extremely good quantitation is possible, as shown in Table 7-3. The data represent nine replicate runs of the separation described in Figure 7-5. The values reported are average retention time and peak area along with their corresponding percent relative standard deviation (% RSD). These results are excellent by any standard of performance. 

The precision of an analysis is most conveniently defined in terms of percent relative standard deviation. The standard deviation is relatively easily calculated following a series of discrete measurements either of absorbance or of concentration. The relative standard deviation is then defined as the standard deviation expressed as a percentage of the mean of the data used to calculate the standard deviation. 

Flame emission techniques generally, require that the monochromator be more strongly resolving than in atomic absorption techniques. In other words the analyst has to use narrower slits in the monochromator. The most effective way to find the best slit to use in a particular instance is to measure the signal-to-noise ratio, that is the percent relative standard deviation for a series of measurements on a suitable standard with each of the slits that are available. The analyst may be surprised to find that in practice the best precision is very often found with extremely narrow spectral bandwidths. This is because unwanted spectral interference is filtered out from the flame. 

NOTE This protocol is based on the assumption that if the 10 unlabeled 2,3,7,8-substituted isomers provided in the EPA standard solutions meet linearity criteria, then the seven additional 2,3,7,8-substituted isomers and the cleanup standard in the CC3 solution may be assumed to have a sufficiently linear response to be used for quantitation. These eight RRFs cannot be used to determine percent relative standard deviation, but are used for percent difference determinations (as described in Paragraph 7.4.6.4) and quantitation of target analytes. 

Relative Response Factor Criteria. Calculate the mean RRF and percent relative standard deviation (%RSD) of the five RRFs (CC1-CC5) for each unlabeled PCDD/PCDF and labeled internal standards present in all five concentration calibration solutions. 

The method was applied directly and easily to the analysis of the pharmaceutical tablet preparations. Mean percent relative standard deviation was foimd to be 0.6231% (Longifene tablet 25 mg). The method was completely validated and proven to be rugged. This validated UV spec-trophotometric method is potentially useful for a routine laboratory analysis because of its simplicity, rapidity, sensitivity, precision, and accuracy. 

Precision refers to the degree of repeatability under the stated conditions of the method. It is expressed as percent relative standard deviation (% RSD) for a statistically significant number of analyses of samples. Precision provides a measure of day to day, analyst to analyst and instrument to instrument variation on a routine basis. The precision data provided in support are standard deviation, % RSD, confidence intervals and may also include inter laboratory variations. 

AND RASMUSSEN Trace Gases in Air and Seawater Table V. Percent Relative Standard Deviation of Compounds on a Capillary Column GC-MS-DS System ... 

As an alternative to the methodologies based on standard deviation, one can define the LOD (or LOQ) to be the lowest concentration that produces an analytical response that meets predefined quality requirements. For example, one might define the LOD as the lowest analyte concentration that produces a percent relative standard deviation (%RSD) of 10%. The LOD can be determined by performing replicate analyses of successively more dilute samples. The LOD could be estimated if one plots percent relative standard deviation vs. the analyte concentration (Fig. 7). 

Fig. 7 Determination of LOD based on a specified performance requirement. In this example, the LOD is defined as the lowest analyte concentration with a percent relative standard deviation of not more than 4%. The interpolated value of LOD is approximately two concentration units. Although the relationship between concentration and percent relative standard deviation shown here is linear, nonlinear relationships between these two variables are likely.

It has been previously noted that it has historically been possible to obtain widely different values for LQD and LOQ, depending on the approach used and the statistical multiplier applied. As the LOD and LOQ concepts have evolved and have become more standardized and harmonized, obtaining such widely varying results is no longer commonplace. A recent study examined LQD and LQQ values obtained for a multianalyte, gradient, UV-based HPLC method by four different techniques, including 1) a performance expectation of percent relative standard deviation less than 5% 2) a plot of standard deviation vs. concentration (ICH approach) 3) use of the 95% Cl of the best-fit regression line and... 

The Coefficient of Variation, or Percent Relative Standard Deviation... 

Our final goal for this exercise is to calculate the coefficient of variation (CV), also known as the percent relative standard deviation (%RSD) (see Section 6B-5 for an explanation of this term). As shown by Equation 6-9 on page 126, the CV is... 

Use a spreadsheet to compare the masses of (a) TRIS (121 g/mol), (b) Na2C03 (106 g/moI), and (c) Na2B407 10H2O (381 g/mol) that should be taken to standardize an approximately 0.020 molar solution of HCl for the following volumes of HCl 20.00 mL, 30.00 mL, 40.00 mL, and 50.00 mL. If the standard deviation associated with weighing out the primaiy-standard bases is O.I mg, use the spreadsheet to calculate the percent relative standard deviation that this uncertainty would introduce into each of the calculated molarities. 

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