Читать книгу Medical Statistics - David Machin - Страница 55

Means and medians convey different impressions of the location of data, and one cannot give a prescription as to which is preferable; often both give useful information. If the distribution is symmetric, then in general the mean is the better summary statistic, and if it is skewed then the median is less influenced by the tails. If the data are skewed, then the median will reflect a ‘typical’ individual better. For example, if in a country median income is £20 000 and mean income is £24 000, most people will relate better to the former number.

It is sometimes stated, incorrectly, that the mean cannot be used with binary, or ordered categorical data but, as we have noted before, if binary data are scored 0/1 then the mean is simply the proportion of 1s. If the data are ordered categorical, then again the data can be scored, say 1, 2, 3, etc. and a mean calculated. This can often give more useful information than a median for such data, but should be used with care, because of the implicit assumption that the change from score 1 to 2, say, has the same meaning (value) as the change from score 2 to 3, and so on.