Relative standard deviations

The combined result of two such determinations yielded a leak size figure of 8.8% of the feed flow (with a relative standard deviation of less than 5%). This figure could sufficiently explain the product quality problems experienced, whose alternative explanation in turn was catalyst poisoning. 

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... 

The relative standard deviation for sampling, Sj r, is obtained by dividing equation... 

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... 

The amount of sample needed to give a relative standard deviation of 2%, therefore, is... 

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

When the target population is segregated, or stratified, equation 7.5 provides a poor estimate of the amount of sample needed to achieve a desired relative standard deviation for sampling. A more appropriate relationship, which can be applied to both segregated and nonsegregated samples, has been proposed. ... 

In Example 7.6 we found that an analysis for the inorganic ash content of a breakfast cereal required a sample of 1.5 g to establish a relative standard deviation for sampling of 2.0%. How many samples are needed to obtain a relative sampling error of no more than 0.80% at the 95% conhdence level ... 

The sampling constant for the radioisotope " Na in a sample ( homogenized human liver has been reported as approximate 35 g. (a) What is the expected relative standard deviation fo sampling if f.O-g samples are analyzed (b) How many f.O-g samples need to be analyzed to obtain a maximum sampling error of 5% at the 95% confidence level ... 

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%. 

Precision For absorbances greater than 0.1-0.2, the relative standard deviation for atomic absorption is 0.3-1% for flame atomization, and 1-5% for electrothermal atomization. The principal limitation is the variation in the concentration of free-analyte atoms resulting from a nonuniform rate of aspiration, nebulization, and atomization in flame atomizers, and the consistency with which the sample is heated during electrothermal atomization. 

Precision When the analyte s concentration is well above the detection limit, the relative standard deviation for fluorescence is usually 0.5-2%. The limiting instrumental factor affecting precision is the stability of the excitation source. The precision for phosphorescence is often limited by reproducibility in preparing samples for analysis, with relative standard deviations of 5-10% being common. 

Precision For samples and standards in which the concentration of analyte exceeds the detection limit by at least a factor of 50, the relative standard deviation for both flame and plasma emission is about 1-5%. Perhaps the most important factor affecting precision is the stability of the flame s or plasma s temperature. For example, in a 2500 K flame a temperature fluctuation of +2.5 K gives a relative standard deviation of 1% in emission intensity. Significant improvements in precision may be realized when using internal standards. 

Precision The precision of a gas chromatographic analysis includes contributions from sampling, sample preparation, and the instrument. The relative standard deviation due to the gas chromatographic portion of the analysis is typically 1-5%, although it can be significantly higher. The principal limitations to precision are detector noise and the reproducibility of injection volumes. In quantitative work, the use of an internal standard compensates for any variability in injection volumes. 

For example, when the activity is determined by counting 10,000 radioactive particles, the relative standard deviation is 1%. The analytical sensitivity of a radiochemical method is inversely proportional to the standard deviation of the measured ac-... 

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 ... 

I which, for an average recovery of 98.1% gives a relative standard deviation of approximately 0.7%. If the acid s concentration is controlled such that its effect approaches that for factors B, C, and F, then the relative standard deviation becomes 0.18, or approximately 0.2%. 

What is the estimated relative standard deviation for the results of a collaborative study in which the sample is pure analyte (100% w/w analyte) Repeat for the case in which the analyte s concentration is 0.1% w/w. 

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. 

A newly proposed method is to be tested for its singleoperator characteristics. To be competitive with the standard method, the new method must have a relative standard deviation of less than 10%, with a bias of less than 10%. To test the method, an analyst performs ten replicate analyses on a standard sample known to contain 1.30 ppm of the analyte. The results for the ten trials are... 

A class of analytical students is asked to analyze a steel sample to determine the %w/w Mn. (a) Given that the steel sample is 0.26% w/w Mn, estimate the expected relative standard deviation for the class results, (b) The actual results obtained by the students are... 

Are these results consistent with the estimated relative standard deviation ... 

A study was conducted to measure the concentration of D-fenfluramine HCl (desired product) and L-fenfluramine HCl (enantiomeric impurity) in the final pharmaceutical product, in the possible presence of its isomeric variants (57). Sensitivity, stabiUty, and specificity were enhanced by derivatizing the analyte with 3,5-dinitrophenylisocyanate using a Pirkle chiral recognition approach. Analysis of the caUbration curve data and quaUty assurance samples showed an overall assay precision of 1.78 and 2.52%, for D-fenfluramine HCl and L-fenfluramine, with an overall intra-assay precision of 4.75 and 3.67%, respectively. The minimum quantitation limit was 50 ng/mL, having a minimum signal-to-noise ratio of 10, with relative standard deviations of 2.39 and 3.62% for D-fenfluramine and L-fenfluramine. 

Investigated is the influence of the purity degree and concentration of sulfuric acid used for samples dissolution, on the analysis precision. Chosen are optimum conditions of sample preparation for the analysis excluding loss of Ce(IV) due to its interaction with organic impurities-reducers present in sulfuric acid. The photometric technique for Ce(IV) 0.002 - 0.1 % determination in alkaline and rare-earth borates is worked out. The technique based on o-tolidine oxidation by Ce(IV). The relative standard deviation is 0.02-0.1. 

To determine of Ce(IV) in acid soluble single crystals, a simple and sensitive method is proposed. The method is based on the reaction of tropeoline 00 oxidation by cerium(IV) in sulfuric acid solution with subsequent measurement of the light absorption decrease of the solution. The influence of the reagent concentration on the analysis precision is studied. The procedure for Ce(IV) determination in ammonium dihydrophosphate doped by cerium is elaborated. The minimal determined concentration of cerium equal to 0.04 p.g/ml is lower than that of analogous methods by a factor of several dozens. The relative standard deviation does not exceed 0.1. 

As the result of the performed investigations was offered to make direct photometric determination of Nd microgram quantities in the presence of 500-fold and 1100-fold quantities of Mo and Pb correspondingly. The rare earth determination procedure involves sample dissolution in HCI, molybdenum reduction to Mo (V) by hydrazine and lead and Mo (V) masking by EDTA. The maximal colour development of Nd-arsenazo III complex was obtained at pH 2,7-2,8. The optimal condition of Nd determination that was established permit to estimate Nd without separation in solution after sample decomposition. Relative standard deviations at determination of 5-20 p.g of Nd from 0,1 g PbMoO are 0,1-0,03. The received data allow to use the offered procedure for solving of wide circle of analytical problems. 

Suggested method characterized by relative standard deviation of 0.02-0.1 allows determination of water in organic solvents until 0.008 mass.%. Concentrations under mentioned above can not be detected by direct GC due to residual humidity of sorbent and parts of chromatographic equipment. 

The complex of the following destmctive and nondestmctive analytical methods was used for studying the composition of sponges inductively coupled plasma mass-spectrometry (ICP-MS), X-ray fluorescence (XRF), electron probe microanalysis (EPMA), and atomic absorption spectrometry (AAS). Techniques of sample preparation were developed for each method and their metrological characteristics were defined. Relative standard deviations for all the elements did not exceed 0.25 within detection limit. The accuracy of techniques elaborated was checked with the method of additions and control methods of analysis. 

A simple, rapid and seleetive eleetroehemieal method is proposed as a novel and powerful analytieal teehnique for the solid phase determination of less than 4% antimony in lead-antimony alloys without any separation and ehemieal pretreatment. The proposed method is based on the surfaee antimony oxidation of Pb/Sb alloy to Sb(III) at the thin oxide layer of PbSOyPbO that is formed by oxidation of Pb and using linear sweep voltammetrie (LSV) teehnique. Determination was earried out in eoneentrate H SO solution. The influenee of reagent eoneentration and variable parameters was studied. The method has deteetion limit of 0.056% and maximum relative standard deviation of 4.26%. This method was applied for the determination of Sb in lead/aeid battery grids satisfaetory. 

In the eourse of the study ICP AES teehnique for determining B, Ba, Ca, Cl, Cu, Ee, K, Mg, Mn, Na, P, S, Se, Si, Sr, and Zn in blood serum is developed. Relative standard deviations vary in the range from 0.02 to 0.25 depending on the element. The eorreetness of results obtained is eonfirmed by eomparing with those of independent analytieal methods. 

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