Standard deviation , calculation for

Finally, it is worth investigating how deterministic values of material strength are calculated as commonly found in engineering data books. Equation 4.14 states that the minimum material strength, as used in deterministic calculations, equals the mean value determined from test, minus three standard deviations, calculated for the Normal distribution (Cable and Virene, 1967) ... 

The threshold of sensitivity varies according to the instrument and the element being considered. Numerous comparative tables on detection limit values exist which are continually being updated as a result of the progress made in instrumentation. The sensitivity threshold corresponds to the minimum concentration of element in solution that will yield an analytical signal for which the amplitude is equal to three times the standard deviation calculated for an analytical blank. This classic definition leads to rather optimistic values and very variable with respect to the element. The detection limit of the instrument represents the concentration of an element, which allows detection with a confidence of 95 per cent (cf. Chapter 22). 

Measures of Central Tendency and Muuation-Mean, Median, and Standard Deviation 585 A5i -1 3 Standard Deviation Calculation for Each Group... 

Statistical weighting is the statistically most straightforward method. The impedance data should be acquired several (n) times and standard deviations calculated for the real and imaginary parts separately using the average impedance Z i at each frequency, i ... 

Stability in sample solution (ST-3). Many solutes (analytes) readily decompose in sample solution prepared prior to TLC investigation. The stability of samples in a final sample solution may be determined from the system stability defined as a measure of bias in the assay results within a preselected time interval (in TLC, every hour up to 4-6 hours) determined by replicate analysis of the same ready-made sample solution, each time using freshly prepared standard solution for comparison. The results are evaluated for major and/or minor components. System stability is considered appropriate if the relative standard deviation calculated for the assay results obtained after different time periods does not exceed more than twice the corresponding value of system precision. If the value is higher, when the assay results are plotted as a function of time, the maximum duration of the usability of a sample solution can be calculated. 

Six repeat titrations went into every mean and standard deviation listed (for a total of 4 x 4 X 6 = 96 measurements). The data in Table 2.17 are for batches A, B, C, and D, and the calculated means respectively standard deviations are for methods 1, 2, 3, and 4. The means for both rows and columns are given. The lowest mean in each row is given in bold. The overall... 

Two models of practical interest using quantum chemical parameters were developed by Clark et al. [26, 27]. Both studies were based on 1085 molecules and 36 descriptors calculated with the AMI method following structure optimization and electron density calculation. An initial set of descriptors was selected with a multiple linear regression model and further optimized by trial-and-error variation. The second study calculated a standard error of 0.56 for 1085 compounds and it also estimated the reliability of neural network prediction by analysis of the standard deviation error for an ensemble of 11 networks trained on different randomly selected subsets of the initial training set [27]. 

Means and standard deviations calculated according to Eqs. (4.9) and (4.12) or the following, respectively, are only characteristic for sample subsets if certain pre-requisites are satisfied, the fulfilment of these can be verified by tests. The observed values of measurement series have to... 

The precision limits r and R are given by equations (4.3a) and (4.3b), respectively, where tv>a is the Student /-value for v degrees of freedom and a corresponds to the stated probability, sr is the repeatability standard deviation and Sr is the reproducibility standard deviation calculated from (v + 1) results ... 

Mean and standard deviation calculated from data from 10 rats per diet group. Corrected by adjusting test diets to 2.50 for casein (AOAC). 

LISTING OP RATE OP VAPORIZATION (G/SBC) AT CONSTANT TEMPERATURE CALCULATION OF AVERAGE VALUES AND STANDARD DEVIATION (EXAMPLE FOR 1 HOUR)... 

The precision of the method calculated as the relative standard deviation (RSD) for five replicates was 2.4% for the level of 30 pg L of aluminum in water. 

If we don t have such an ideal control sample, but only one with a matrix different from the routine sample (e.g. a standard solution) than we have to consider also the uncertainty component arising from changes in the matrix. For this purpose we use the (repeatability) standard deviation calculated from repeated measurements of our routine samples (performed e.g. for a range control chart). When we estimate the reproducibility within laboratory we now have to combine both contributions by calculating the square root of the sum of squares. 

To measure the thermal expansion coefficients, a 0.125 in. thick sample was taken from the cured plates. The Increase in length with temperatures was measured by use of a Dupont 941 Thermomechanical Analyzer (TMA), with a heating rate of 5°C/min. The instrument was calibrated with an aluminum standard. Three runs were made for each sample and standard deviations calculated. 

Method Performance. A blank sample, prepared using the same procedure as for the samples, was included with every five samples. PCB 28 and y-HCH were the only compounds detected in the blanks. Detection limits, calculated as mean blank +3 SD, were typically 2.3-13.3 pg/pF = 0.02-0.12 ng/g soil. Results were not blank corrected. Replicate analysis (the same soil sample extracted three times) was done for several samples. The relative standard deviation (RSD) for replicate analysis was always less than 20% (n = 3). Analytical recoveries were monitored with the aid of two recovery standards mirex for FI and 5-HCH for F2. The mean recovery for mirex was 100 ... 

For the sake of illustration the constant relative standard deviation (cvj for the three variable components was set to 5%. The demands concerning the calculation of the robustness coefficient were to have a deviation in the crushing strength (6> ) of ION at most with a reliability (m ) of 0.95. 

The means and standard deviations (SD) for the organic acids in the QC samples are calculated from ten interassay values for each control, and used for QC purposes... 

An established external quality control (QC) scheme is not currently available. Pooled disease control CSF retained from other analyses is used. Aliquots of the pooled CSF are made and stored at -70°C. This CSF is analysed on five separate occasions and the mean and standard deviation determined. For an analytical/diagnostic run to proceed, analysis of QC material must provide concentration values that are within two standard deviations (plus and minus) of the calculated mean for that particular QC. Construction of Levy-Jennings type control charts provide historical information of overall performance and highlight potential deterioration in the performance of the system. 

Tschebycheff s Inequality. An average x for each of the "fingerprint" elements was calculated for the Florida group and is listed in Table VIII along with the corresponding standard deviation (s). For an unknown sample a deviation a is calculated from... 

The standard deviation (SD) for activity of 137Cs is calculated from... 

For Data Table 6.2, calculate the count rate, R, in counts per second (cps) and the respective standard deviation (a) for each count in each type... 

Follow we discuss the implementation of the %2 analysis in an Excel spreadsheet. It deals with the emission decay of a solution with two emitters of slightly different lifetimes. Measurements are done at one wavelength only. Column C of the Excel spreadsheet shown in Figure 7.10 contains the estimated standard deviation standard deviation is simply the square root of the intensity. Column D contains the calculated intensity as the sum of two exponential decays. 

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