Indicators of central tendency

To indicate the first of these, we quote an indicator of central tendency and for the second an indicator of dispersion . 

Indicators of central tendency how large are the numbers Indicators of dispersion how variable are the numbers ... 

Indicators of central tendency - mean, median and mode... 

The term indicator of central tendency describes any statistic that is used to indicate an average value around which the data are clustered. Three possible indicators of central tendency are in common use - the mean, median and mode. 

There is a definite pecking order among the three indicators of central tendency described above. The mean is the industry standard and is the most useful for a whole range of further purposes. Unless there are specific problems (e.g. polymodality or marked skewness), the mean is the indicator of choice. The median is met with pretty frequently and the mode (or modes) tends only to be used when all else fails. 

The second quartile (median) as an indicator of central tendency The second quartile has half the observations above it and half below and is therefore synonymous with the median. We have already established that the median is a useful and robust indicator of central tendency, especially when there are some extreme... 

Just as the median is a robust indicator of central tendency, the interquartile range is a robust indicator of dispersion. Take the longest half-life seen with steroid 1 (15.8 h) and consider what would have happened if that individual had produced a half-life of 100 h (or any other extreme value). The answer is that it would make absolutely no difference to the inter-quartile range. The value of 15.8 h is already something of an outlier, but it had no undue effect on the inter-quartile range. 

Median and inter-quartile range are robust indicators of central tendency and dispersion... 

The mean, median and mode are all indicators of central tendency and tell us about the magnitude of the figures within our data. 

The three quartile values indicate the figures that appear 25, 50 and 75 per cent of the way up the list of data when it has been ranked. The second quartile is synonymous with the median and can act as an indicator of central tendency. The interquartile range (difference between first and third quartile) is an indicator of dispersion. The median and interquartile range are robust statistics, which means that they are more resistant to the effects of occasional extreme values than the mean and SD. The robustness of the median can be abused to hide the existence of aberrant data. 

Statistical indices are fundamental numerical quantities measuring some statistical property of one or more variables. They are applied in any statistical analysis of data and hence in most of Q S AR methods as well as in some algorithms for the calculation of molecular descriptors. The most important univariate statistical indices are indices of central tendency and indices of dispersion, the former measuring the center of a distribution, the latter the dispersion of data in a distribution. Among the bivariate statistical indices, the correlation measures play a fundamental role in all the sciences. Other important statistical indices are the diversity indices, which are related to the injbrmationcontentofavariahle,the —> regressiowparameters, used for regression model analysis, and the —> classification parameters, used for classification model analysis. 

Indices of central tendency (or location) provide a single value of a variable that is the most central and typical for representing the set of observations or a distribution. 

Fig. 4.3 Probability density or relative frequency curve showing three parameters indicative of central tendency...

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