Kahjin’s Weblog


Posted in 未分類 by kahjin on 3月 14, 2008


More generally, averages by themselves neglect variation in the data and may imply more uniformity than exists. For example, the average temperature on the planet Mercury of about 15o F does not sound too bad—until one considers that it swings from 300o F above to almost 300o F below zero. The neglect of variation can be particularly misleading when averages are compared. For example, the fact that the average height of men is distinctly greater than that of women could be reported as “men are taller than women,” whereas many women are taller than many men. To interpret averages, therefore, it is important to have information about the variation within groups, such as the total range of data or the range covered by the middle 50 percent. A plot of all the data along a number line makes it possible to see how the data are spread out.



We are often presented with summary data that purport to demonstrate a relationship between two variables but lack essential information. For example, the claim that “more than 50 percent of married couples who have different religions eventually get divorced” would not tell us anything about the relationship between religion and divorce unless we also knew the percentage of couples with the same religion who get divorced. Only the comparison of the two percentages could tell us whether there may be a real relationship. Even then, caution is necessary because of possible bias in how the samples were selected and because differences in percentage could occur just by chance in selecting the sample. Proper reports of such information should include a description of possible sources of bias and an estimate of the statistical uncertainty in the comparison.


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