Median vs. Average to Describe
What is the median and
how is it different from the 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