The five readings 7, 9, 12, 15 and 20 have median 12. Two further readings, 4 and 30, are added to the set. What is the median of the seven readings?

In order the seven readings are 4, 7, 9, 12, 15, 20, 30, and with an odd count the median is the 4th of them, 12 — exactly where it was. One new reading arrived below the old middle and one above it, so the middle simply stayed put. The value 13.5 = (12 + 15)/2 averages two middle readings as though the count were still even; 15 is the 5th reading and 9 the 3rd. The MEAN is not so calm: it moves from 63 ÷ 5 = 12.6 to 97 ÷ 7 ≈ 13.86, because every value pulls on it.