Standard deviation weighing

VOLUME.dat Section 1.1.2 A set of five precision weighings of a water-filled 100 ml flask the weights in grams were converted to milliliters using the standard density-vs.-temperature tables. Use with MSD to test the effect of truncation errors on the calculation of the standard deviation. (See Table 1.1.)... 

Most pharmacopoeias include a simple weight test on a specified number of tablets that are weighed individually. The arithmetic mean weight and relative standard deviation (i.e., mean divided by standard deviation) of these tablets is then calculated. Only a specified number of test tablets may lie outside the prescribed limits. These specifications vary depending upon the type of tablet and amount of active present. 

We have found that it is essential to measure physical properties carefully. The solid fraction was determined in each case from the mass and thickness of circles cut to an accurately known size (using a lathe in the case of BOM). The thickness was measured with a micrometer. The mass was determined with standard deviation about 0.5% (from three weighings). The wire diameter and screens mesh dimensions were measured from photomicrographs and from the specifications given by manufacturers. The front-to-back measurement will be described below. 

The standard uncertainty arising from random effects is typically measured from precision studies and is quantified in terms of the standard deviation of a set of measured values. For example, consider a set of replicate weighings performed in order to determine the random error associated with a weighing. If the true mass of the object being weighed is 10 g exactly, then the values obtained might be as follows ... 

The use of a special microtechnique has permitted the precipitation, weighing, and determination of about 2 /xg of technetium with a standard deviation of 0.08 /xg . The precipitate is filtered, washed with ice-cold water, dried at 110 °C and weighed as (CgH5) AsTcO. Permanganate, perchlorate, periodate, iodide, fluoride, bromide, thiocyanate anions and mercury, bismuth, lead, silver, tin and vanadyl cations as well as nitrate concentrations above 0.5 M interfere with the determination. 

If a certain analysis is frequently carried out, it may be advantageous to keep in stock some well-mixed bulk samples (low, medium and high range values), sub-samples of which should be included with every fresh batch of analyses, and again well-mixed before weighing. After a statistically significant number of analyses, an accepted average value for the bulk sample is obtained, and the amount of scatter of results computed as a standard deviation, s, where... 

Repeatability Obtain as standard deviation of repeated weighings or assume part of repeatability of measurement = s. = 0.2 mg... 

The manufacturer s calibration information must now be accounted for. You might be lucky and have a 10-mL pipette that is indeed 10.00 mL, but the manufacturer is only guarantees the pipette to be not less than 9.98 mL and not more than 10.02 mL. As the pipette is used throughout many experiments, then this possible systematic effect will not dissipate with repeated measurements and must be accounted for. There are two alternatives. The first is to calibrate the pipette in the laboratory. The fill-and-weigh experiments that would give the standard deviation of the measurement will also, from the mean, give an estimate of the volume of the pipette (see spreadsheet 6.1). 

Suppose with 10 fill-and-weigh experiments, the mean volume of a pipette is 10.0131 mL with a standard deviation of s = 0.0019 mL. The standard deviation of the mean is 0.0019/ /10 = 0.0006 mL. In future use of this... 

Analysis of Acidic Functional Groups. CARBOXYL GROUP ANALYSIS. Carboxyl groups of the samples were determined by modifications of methods developed by Perdue et al. (12). Accurately weighed samples of approximately 10 mg were used for this determination. Eleven analyses of an aquatic humus sample gave a mean value of 4.76 meq/g a standard deviation (s) of 0.14 and a coefficient of variation (cv) of 2.9 were calculated. 

An example of a mixture of 1-mm-diameter particles of KC1 and KN03 in a number ratio 1 99 follows Equation 28-4. A sample containing 104 particles weighs 11.0 g. What is the expected number and relative standard deviation of KC1 particles in a sample weighing 11.0 X 102g ... 

The density of a liquid is measured by filling a 50 ml flask as close as possible to the index mark and weighing. In successive trials the weight of the liquid is found to be 45.736 g, 45.740 g, 45.705 g, and 45.720 g. For these weights calculate the average deviation, the standard deviation, the 95% confidence interval for a single value, and the 95% confidence interval for the mean. 

Example 3 Determining the estimated standard deviation. What is the estimated standard deviation for five weighings of a sample with the following values 18.5, 18.4, 18.6, 18.3, andl8.7 What is the estimated standard deviation of the mean for this sample ... 

Knowledge of statistics (Chapter 26) is basic to effective handling of the last unit operation, evaluation of data. Many chemists rarely go beyond a calculation of the standard deviation for a set of determinations and have the erroneous notion that the use of more advanced statistical methods is restricted to enormous bodies of data. A point often overlooked is that a relatively small number of systematically planned observations may yield more information than a larger number of repeated identical observations. For example, in the simple matter of running triplicate analyses of a sample, it may be best to weigh three samples of substantially different sizes. The results obtained may reveal determinate errors that would be unsuspected with samples of equal size. 

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