No. Median is a value of a specimen that at least half of the population is not smaller than it and at least half is not greater than it. In typical cases of la

No. Median is a value of a specimen that at least half of the population is not smaller than it and at least half is not greater than it. In typical cases of large(-ish) populations with a range of values the notion of "precisely half of the population is smaller" is just a mental model good enough to generally understand what the median is about. Now imagine a degenerated case of a population with the same score. Surely there is a median, but surely none of the specimen is smaller than the median. A little less trivial case is a population of five with one value below, one value above, and three values in the middle.