Interval Estimation of a Median

The non-existence is proved of a procedure giving a confidence interval for a median with a distribution- free confidence coefficient higher than that of the variation interval of the sample. On the other hand a procedure is given the confidence coefficient of which does not fall below an arbitrarily prescribed level for any symmetric unimodal distri- bution. This procedure can also be considered as an interval estimation method for the mode, and its behaviour in this role is studied within the class of unimodal (but not necessarily symmetric) distributions.