When is the average snowfall not the amount to expect?For most people, the average represents a value obtained by taking a set of values, adding them, then dividing by the number values. In stricter statistical terms this is the "mean". An average can be any of several measures of central tendency, including the "median" or the "mode". The median is a value such that half the numbers are above that value and half are below it. The "mode" represents the most frequently occurring value. The median is often a better representation of an "expected value" than the mean since the mean is more sensitive to the affects of outlining or extreme values.
If the mean seasonal snowfall for a location is 60 inches but the median is 65, then the majority of the seasons in the climatological record experienced above average snowfall. You would thus "expect" to get 65 inches per season rather than 60 but you would also expect to have an occasional year where snowfall is severely lacking. These much lower values skew the average down from the amount that would typically occur.
The opposite condition as just previously described occurs if the median were 55 rather than 65. Most seasons would feature below average snowfall with a fewer seasons producing well above average snowfall.
The "Frequently Asked Questions" section on the National Climatic Data Center's Climate Normals page provides a good discussion about what normals really are and how they are not necessarily indicative of the weather you should expect. See in particular the entries entitled "What is a Climate Normal?" and "Is a Normal the Climate You Would Expect?".