Six readings were recorded as 9, 11, 14, 16, 18, 21. Later the reading 14 was found to be a mis-entry whose correct value is 30. What is the effect of the correction on the mean and on the median?

Before the correction the six values total 89, so the mean is 89/6, and the median is the average of the middle pair, (14 + 16)/2 = 15. Replacing 14 by 30 adds 16 to the total, giving 105 and a mean of 105/6 = 17.5, a rise of 16/6 = 8/3. In order the corrected data read 9, 11, 16, 18, 21, 30, so the middle pair becomes 16 and 18 and the median rises to 17, a rise of 2. The whole rise of 16 does not go to the mean — it is shared among all six observations — and the median is not always immune to a correction, because here the corrected value crossed the middle of the data.