I have an apple weighing 150 g. and an orange weighing 145 g. Which fruit is unusually heavier? One would argue that, based on the absolute weight of the fruits, the apple is heavier. But then you are comparing apples with oranges!
A proper comparison is only possible if you standardise the weights and bring them to the same page. In other words, we use Z-score and compare them on a standard normal distribution. If X is the measurement, mu is the mean of the population where the sample belongs, and sigma is the standard deviation.
Once the Z-scores are estimated, one can place it over a standard normal distribution. Note that we have made the assumption that the weights of apples and oranges follow normal distributions.
Suppose the following are the parameters of those fruits.
| Apple | Orange | |
| Mean (g) | 160 | 140 |
| Standard Deviation (g) | 15 | 20 |
Z-scores are obtained by applying the equation.
| Apple | Orange | |
| Z | (150-160)/15 = -0.66 | (145-140)/20 = 0.25 |
So the orange is heavier than usual.
