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If you need to reduce a distribution to a single number, the most informative number is going to be the mean. Not necessarily. If you want an general-purpose s
by simonster 13y ago
If you need to reduce a distribution to a single number, the most informative number is going to be the mean.
Not necessarily. If you want an general-purpose summary statistic that's easy to interpret, for many distributions, the median is a better statistic than the mean. (The pathological case is the Cauchy distribution, which looks like a normal distribution with heavier tails, but has a median but no mean, and both any individual data point and the sample mean approximate the median of the true distribution equally well.)
But yes, unless you have an a priori reason to think that the response is normal, it is worthwhile to look at quantiles, a histogram, or a kernel smoothed density estimate of the data as opposed to a single statistic.