Which average is calculated in a way that uses every value in the data set, so that changing any one value must change the result?

Explanation

The total of a data set contains every value, and the mean is that total shared between the values, so altering any value alters the answer. Ordering the data to find the median does look at every value, but only the central position survives into the result, and the largest value could be doubled without moving it at all.