Median vs. Average to Describe Normal
What is the median and how is it different from the average?
Although average is a commonly-used and well understood statistic, median is also a common descriptor used to express a “middle” value in a set of data. This “middle” value is also known as the central tendency. Median is determined by ranking the data from largest to smallest, and then identifying the middle so that there are an equal number of data values larger and smaller than it is. While the average and median can be the same or nearly the same, they are different if more of the data values are clustered toward one end of their range and/or if there are a few extreme values. In statistical terminology, this is called skewness. In this case, the average can be significantly influenced by the few values, making it not very representative of the majority of the values in the data set. Under these circumstances, median gives a better representation of central tendency than average.
Why is the median preferable for SWE?
In general, snow water equivalent (SWE) for a given day over a historical period shows skewness. This is particularly evident at the onset of snow accumulation and near the time of melt out, when many years have very small or zero values and only a few have significant nonzero values. Skewness may also be noticeable throughout the year due to the presence of a few large snow years. In these cases, the median is typically different (usually smaller) than the average but better represents the central tendency of SWE than does the average. These effects are illustrated in the graphic.