Outlying values

The median of a set of numbers arranged in order of magnitude is the middle value or the arithmetic mean of the two middle values. The median allows inclusion of all data in a set without undue influence from outlying values it is preferable to the mean for small sets of data. 

In describing the average diameter of a sample, three parameters can be used the mean, the median, and the mode. The mean is the sum of all diameters divided by the total number of particles. It is sensitive to extreme values and thus is often not particularly useful. The median is the value above and below which 50% of the particles are found. It is less influenced by outlying values and is preferable to the mean as a single measure of particle size. The mode represents the size occurring most frequently it is used less frequently than the mean or the median. In a perfectly symmetrical distribution, the mean, median, and mode values are the same. 

Where risks are higher that normally acceptable and all reasonable mitigation measures have been examined to find out value and practicality, the principal of risk as low as reasonably practical applies. Where the available risk protection measures have been exhausted and the risk level is still higher that the accepted numerical value, the risk would be considered "As Low As Reasonably Practical" (ALARP). 

The measured /out versus /data characteristics for different FDD values (20, 25, 30 V) are shown in Figure 9.10c, where solid and open symbols correspond to /out measured during select and deselect times. The peak current flow for /out during the select time transition is excluded in Figure 9.10c. For the deselect time /out values, the median values with error bars... 

The final R-factor and structural parameters exceed the standards described in Section I and attest to the high quality of this model. Atom locations are precise to an average of 0.34 A. about one-fifth of a carbon-carbon covalent bond length. The plot of temperature factors shows greater variability and range for side-chain atoms, as expected, and shows no outlying values. The model defines the positions of all amino-acid residues in the protein. 

Grubbs statistic is compared with the critical values in Table 6.5. If the Grubbs statistic is significant at a probability of 5 percent, the outlying values are considered stragglers. Values are considered outliers if significant at the 1 percent level. 

Show how quartiles can be used to convey information similar to that mentioned above, even in the presence of extreme outlying values... 

The middle ranking value. Especially useful with data containing occasional highly outlying values. It is robust (resists the influence of aberrant data). 

When choosing a descriptive statistic we need to be aware of whether the data contains extreme outlying values and whether it forms a single cluster (unimodal) or several (polymodal). We should also think about what use is intended for the statistic we quote. 

For Table 4.2, the SEM for Alpha is 1.98 mg and for Bravo only 0.996 mg. The sample of tablets from the Alpha machine is liable to be distorted by somewhat outlying values and so the SEM is relatively high. In contrast, the mean based on the tablets from the Bravo machine will be more reliable as it is less likely to contain badly outlying values and the SEM is correspondingly lower. 

Yet there are circumstances in which single gross errors contaminate otherwise valid assays, and it is desirable to be able to delete such errors and use the remaining repetitions of the assay. How can we tell when to delete such outlying values, and when it is necessary to retain them and accept the possibility that our assay is less precise than we had hoped ... 

The first and best approach should be to examine the assay procedure that was used to try to find an explanation (e.g., a technical error or even a data recording error) for the outlying value. If a substantial technical error is found, then the outlying value may be discarded, and if possible the assay should be run again to replace it. If no such explanation is found, however, we still may wish to discard grossly aberrant values rather than repeat the entire set of n repetitions of the assay. One approach... 

Calculate the mean and SD for all observations other than the outlying value. 

Subtract the calculated mean from the outlying value, and divide by the calculated SD. For the data above, this yields (1.530 -0.483)/0.024 = 43.6. 

Discard the outlying value if the absolute value of this number is too large. In other words, the outlying value is discarded when it is too far from the mean of the other values, in units of their SD. 

Conclusions should always be tempered by the possible importance of untested or uncontrolled variables, and by the risks assumed in the testing protocol. The problem of outlying values and their effects needs to be considered also. Retrospective correlations of historical data are frequently employed with no consideration of weighting for unbalanced distributions, with the result that one often ends up with merely a mathematical description of random error. Finally, as noted above, there is the danger of comparisons at fixed points, or at fixed sets of... 

Phenomenologically, as the olefin concentration is Increased at a given triphenylmethyl concentration, the rates maximize and then descend slowly. At high olefin concentrations the rates decrease toward the lined out value with olefin alone. The deleterious effect of too high olefin concentrations may be partially offset by increasing the triphenylmethyl level. 

Brazilian Amazon basin was calculated for each soil type by multiplying the mean C stocks by the area of each soil type from a digitized soil map at scale 1 5,000,000 (Empresa Brasileira de pesquisa Agropecuaria, 1981). The authors determined that 47 Pg of carbon is stocked in the first soil meter, of which 44% is in the upper 20 cm. Cerri et al. (2000) also showed that if the standard deviation is used for evaluating the accuracy of estimates, the associated error would be 11.6 Pg of carbon, i.e. 24.5% of the mean value. The use of means is subject to caution, even more when the number of samples is reduced. As the sample size for most of the soil types is less than 30, outlying values may have a marked influence on the mean. The calculation with the median values, because it is less sensitive to extreme values. 

As previously pointed out, values of r and /3 depend on the maimer in which the gas is liberated. In the procedure to be described the pressure is reduced in 200 psi steps from the bubble point to atmospheric pressure and the gas bled off after each step. The values of r... 

TRAPS OR LIQUID COLLECTION DRUMS. GAUGE GLASS. DRAIN OUT VALUE, HIGH LIQUID LEVEL ALARM CONTACTS TO BE FURT ISHED BY COMPRESSOR MANUFACTURER PURCHASER... 

WHO uncertainty in rejported values is the standard deviation of at least six analyses for each intercomparison sample. IAEA uncertainty is the standard error for the values reported by various laboratories after exclusion of outlying values using Chauvenet s criterion. 

United Nations Millennium Summit. This largest ever gathering of world leaders adopted the United Nations World Summit Declaration, which spells out values and principles, as well as goals in key priority areas. World leaders agreed that the UN s first priority was the eradication of extreme poverty and highlighted the importance of a fairer world economy in an era of globalization, http //www.un.org/millennium/summit.htm... 

The problem of minimizing functions is ubiquitous in many different branches of science. It arises very naturally and rather directly in the electronic structure theory when the strategy adopted is variational for, the basic task in the variational approximation boils down to finding out values of a set of parameters present in the trial wavefunction (assuming expansion in terms of finite dimensional analytic... 

---