A more subtle reason why climatological averages may be misleading example has to do with the statistical distribution of individual variables, for instance rainfall. Let us assume daily rainfall amounts were recorded over a certain period (say April, between 1991 and 2020) . This is 30 monthly values varying between 0.0 mm and, for example, 123.2 mm. The values are not regularly distributed over the 0.0-123.2 mm range. Instead, values will be grouped at the lower end, with some high values. Particularly during dry periods as well as in semi-arid and arid areas , rainfall by no means follows a bell-shaped curve. Instead, it follows a distribution with many low values and along tail with some high values. In practice, this usually referred to as an Incomplete gamma distribution., of which the bell-shaped curve and some others (Pearson type III curves) are particular cases. This is why, for many variables such as rainfall, the arithmetic mean, including the climatological average, do not represent the expected value or the most likely value.This occurs whether there is a long term trend or not. If there is no trend, normality and expectation may sometimes overlap. But not necessarily. The sequence of the observations of total April rainfall over 15 years would be something like the sequence below from year 1 to year 15 (to simplify, the unit, mm, will not be repeated for individual values) 0.6, 0.0, 3.0, 0.0, 123.2, 0.2, 0.0, 6.5, 22.1, 0.0, 0.0, 0.8, 0.0, 5.2, 0.4. The values can also be ranked: 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ,0.2 ,0.4 ,0.6 ,0.8 ,3.0, ,5.2 ,6.5 ,22.1 ,123.2. The average is 10.8 mm, but the median is 0.4 mm. The median is the value in the “middle”, i.e. there are 7 values below 0.4 (0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ,0.2) and 7 values above (0.6 ,0.8 ,3.0, ,5.2 ,6.5 ,22.1 ,123.2). When the median and the average are very different, the climate observations are “skewed“.