A negative weight gain would be a weight loss. To understand the concept, suppose \(X \sim N(5, 6)\) represents weight gains for one group of people who are trying to gain weight in a six week period and \(Y \sim N(2, 1)\) measures the same weight gain for a second group of people. The z-score allows us to compare data that are scaled differently.
Therefore, \(x = 17\) and \(y = 4\) are both two (of their own) standard deviations to the right of their respective means. This means that four is \(z = 2\) standard deviations to the right of the mean.
