A data set consists of the values 12, 15, 18, 22, and 25. If the values 1 and 100 are added to the data set, what is the median of the new…

Sort the seven values: 1, 12, 15, 18, 22, 25, 100. With seven values, the median is the 4th value, which is 18. The original five values (12, 15, 18, 22, 25) also had median 18. Adding one very small and one very large value does not move the middle, because the median depends only on position, not on how extreme the outliers are. A common wrong answer is 24 or 28, which come from computing the mean, which is strongly affected by the value 100. Another is 16.5, from averaging the wrong pair of middle values as if there were an even count.