• Story Name: Distribution Patterns
  • Story Topics: Miscellaneous,
  • Datafile Name: Distribution Patterns
  • Methods: Outlier, Summary Statistics, Mean, Median, Histogram, Boxplot,
  • Abstract:

    This "story" illustrates some of the different distribution patterns that variables may take on. The distribution of Tobin's Q-ratios for firms shows high positive skewness. Sometimes this can be 'remedied' by taking the logarithms of the data. Try this for the Q-ratios. Other distributions take on a symmetrical shape resembling the normal distribution. The 29 measures of the density of the earth (Distr #4) is a case in point. Still other distributions, while symmetrical, may be flat compared to the normal distribution or, on the other hand, more peaked that the normal. The breaking strengths of yarn (Distr #2) illustrate the peaked, or leptokurtic, distribution pattern. The outliers at both ends of the distribution suggest that from time to time factors not customarily present in the yarn production process act to produce extreme variation from intended results. A quality control problem may be present. The ages of officers attaining the rank of colonel exhibit a pattern of negative skewness (Distr #3). There appear to be more 'whizzes' than 'laggards.' Students are encouraged to study the summary statistics for these distributions, noting the location of the mean compared to the median, and the distances of the first and third quartiles from the median. Both of these factors are reflections of the direction and degree of skewness in a distribution.

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