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Range variance

At high Reynolds number and for Schmidt numbers near unity or larger, we are justified in assuming that Tt is nearly independent of Schmidt number. We will also need a closure for in (3.175). In general, the dissipation-range variance scales as Re, 1 = Rc, 1/2 (Fox and Yeung 1999 Vedula 2001). We will thus model the covariances by... [Pg.116]

Figure 5.10 Effect of range variance on tower size factor. Figure 5.10 Effect of range variance on tower size factor.
Here, the objective is to quantify the spread of the data about the centre of the distribution. The principal measures of dispersion are the range, variance, standard deviation and coefficient of variation. [Pg.267]

Descriptive statistics Used to summarize information and for the comparison of numbers in different sets of data mean, median, mode, range, variance, standard deviation are descriptive statistics. [Pg.266]

Until the mid-1990s, the CSD base archived 4079 derivatives of cyclopentadienyl and cyclopentadiene bound to almost all elements from Li to Tl. Table 21 presents the values of HOMA index estimated as a mean value for the subsamples built up of the compounds of cyclopentadiene or cyclopentadienyl moieties with particular elements. In most cases the data observed are greatly dispersed hence, statistical characteristics are given as averages and the interquartile ranges of HOMA values as well as the mean C—X interatomic distances are given with their interquartile ranges (variances could not be used for... [Pg.23]

Commonly used descriptive statistics include measures that describe where the middle of the data is. These measures are sometimes called measures of central tendency and include the mean, median, and mode. Another category of measures describes how spread out the data is. These measures are sometimes called measures of variability and include the range, variance, and standard deviation. Additional descriptive measures can include percentages, percentiles, and frequencies. In safety performance measurement, the safety professional must determine the format of the data (i.e., ratio, interval, ordinal, or categorical) that will be collected and match the data format to the appropriate statistic. As will be discussed in the following sections, certain descriptive statistics are appropriate for certain data formats. [Pg.24]

There are three measures of variability. These measures indicate the spread of the data and are the range, variance, and standard deviation (Hays 1998, 171-76). Measures of variability provide the safety manager with an indication of how much the obtained results are spread out. For example, suppose a safety manager collects information on the number of lost days for three employees. The days lost are 1,1, and 2 (that is, they range from 1 to 2 days). The measures of variability would be small compared to three employees who lost 1,10, and 50 days (a range spread from 1 to 50 days). For various statistical procedures, the degree of variation in the data can impact the decision as to whether the results are significant or not. [Pg.25]

Descriptive Statistics statistical techniques that are used to describe the population or sample. Commonly used descriptive statistics include measures of central tendency mean, median and mode and measures of variability range, variance and standard deviation. Additional descriptive measures can include percentages, percentiles and frequencies. [Pg.163]

Central tendency mean, median, and mode Variability range, variance, standard deviation... [Pg.181]

This chapter will be about applications. It will avoid the specifics of the chemistry of near-infrared reflectance spectroscopy (NIRS), and of chemometrics. It will attempt to illustrate in one locus the variables that can affect application of NIRS to grains and seeds and their derived products. Over 50 factors associated with the grains and seeds themselves have been identified (1), any of which can interact to complicate the operation. To confuse the picture yet further is the fact that they may interact in different ways, to different degrees, and under different conditions (of temperature, etc.) and may not even interact at all. Application of NIRS to grains and seeds is complicated by the wide-ranging variance in their size, shape, color, density, composition and texture. [Pg.165]

Table 2. Percentage error for LN compared to reference Langevin trajectories (at 0.5 fs) for energy means and associated variances for BPTI over 60 ps at 7 = 20 ps At = 0.5 fs, Atm = 3 fe, and At — k2Atm, where hz ranges from 1 for LN 1 to 96 for LN 96. Table 2. Percentage error for LN compared to reference Langevin trajectories (at 0.5 fs) for energy means and associated variances for BPTI over 60 ps at 7 = 20 ps At = 0.5 fs, Atm = 3 fe, and At — k2Atm, where hz ranges from 1 for LN 1 to 96 for LN 96.
Precision is a measure of the spread of data about a central value and may be expressed as the range, the standard deviation, or the variance. Precision is commonly divided into two categories repeatability and reproducibility. Repeatability is the precision obtained when all measurements are made by the same analyst during a single period of laboratory work, using the same solutions and equipment. Reproducibility, on the other hand, is the precision obtained under any other set of conditions, including that between analysts, or between laboratory sessions for a single analyst. Since reproducibility includes additional sources of variability, the reproducibility of an analysis can be no better than its repeatability. [Pg.62]

The data we collect are characterized by their central tendency (where the values are clustered), and their spread (the variation of individual values around the central value). Central tendency is reported by stating the mean or median. The range, standard deviation, or variance may be used to report the data s spread. Data also are characterized by their errors, which include determinate errors... [Pg.96]

Report the mean, median, range, standard deviation, and variance for these data. [Pg.98]

As can be seen from Figure 4, LBVs for these components are not constant across the ranges of composition. An iateraction model has been proposed (60) which assumes that the lack of linearity results from the iateraction of pairs of components. An approach which focuses on the difference between the weighted linear average of the components and the actual octane number of the blend (bonus or debit) has also been developed (61). The iadependent variables ia this type of model are statistical functions (averages, variances, etc) of blend properties such as octane, olefins, aromatics, and sulfur. The general statistical problem has been analyzed (62) and the two approaches have been shown to be theoretically similar though computationally different. [Pg.188]

Hydrostatic drives allow for selection of any travel speed up to the maximum without a concurrent variance in engine speed. The engine can be operated at the governed speed to provide proper operating speeds for auxiliary elements, eg, the threshing section of a combine. A frill range of travel speeds is available to adjust to terrain or crop conditions. Industrial applications for hydraulic systems and hydrostatic transmissions include the following (16) ... [Pg.271]

Fig. 8. Plot of data from patients having Hver diseases A or B or unknown X (a) on two blood enzymes (b) scores of points on the first two eigenvectors obtained from an eight-dimensional enzyme space and (c) eigenvector plot of the variance weighted data. Variance weights ranged from 3.5 to 1.2 for the eight blood enzymes measured. A weight of 1.0 indicates no discrimination information (22). Fig. 8. Plot of data from patients having Hver diseases A or B or unknown X (a) on two blood enzymes (b) scores of points on the first two eigenvectors obtained from an eight-dimensional enzyme space and (c) eigenvector plot of the variance weighted data. Variance weights ranged from 3.5 to 1.2 for the eight blood enzymes measured. A weight of 1.0 indicates no discrimination information (22).
Other measures of efficiency are derived from the experimental RTD, which is characterized at least approximately by the variance This quantity is zero for plug flow and unity for complete mixing, and thus affords natural bounds to an efficiency eqiiated to the variance. It is possible, however, for the variance to fall out of the range (0,1) when stagnancy or bypassing occurs. [Pg.2082]

The random nature of most physieal properties, sueh as dimensions, strength and loads, is well known to statistieians. Engineers too are familiar with the typieal appearanee of sets of tensile strength data in whieh most of the individuals eongregate around mid-range and fewer further out to either side. Statistieians use the mean to identify the loeation of a set of data on the seale of measurement and the variance (or standard deviation) to measure the dispersion about the mean. In a variable x , the symbols used to represent the mean are /i and i for a population and sample respeetively. The symbol for varianee is V. The symbols for standard deviation are cr and. V respeetively, although a is often used for both. In this book we will always use the notation /i for mean and cr for the standard deviation. [Pg.277]

Work done by Wiesner [6] is a much more accurate approach. The subject has also been reported on more recently by Simon and Bulskamper [71. They generally agree with Wiesner that the variance of performance with Reynolds number was more true at low value that at high values. The additional influence above a Reynolds number of 10 is not much. It would appear that if a very close guarantee depended on the Reynolds number to get the compressor within the acceptance range (if the Reynolds number was high to begin with), the vendor would be rather desperate. [Pg.426]

The standard deviation of the extra-column dispersion is given as opposed to the variance because, as it represents one-quarter of the peak width, it is easier to visualize from a practical point of view. It is seen the values vary widely with the type of column that is used, (ag) values for GC capillary columns range from about 12 pi for a relatively short, wide, macrobore column to 1.1 pi for a long, narrow, high efficiency column. [Pg.289]


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See also in sourсe #XX -- [ Pg.108 ]




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