Statistic Definition Explanation
Mean Standard arithmetic average;
(a1 + a2 + ... + an)/n		 The mean is the standard statistic we all know and love, and the one which is used on the professor evaluation pages. Surprisingly, it's not a very good "summary statistic" because it gives equal weights to every evaluation. But, it's what we use most commonly because it's how we're graded as students and it's a statistic everyone knows and understands.
Median The "center" value of the ordered data set. If we were looking at seven evaluations and put the scores students gave those professors in order for those seven evaluations, the median values would be the fourth evaluation. A better summary statistic to provide the center of a distribution of values. Only moderately applicable to the way professors are rated, though beacuse the majority of distributions found here are multi-model (i.e. they have numerous centers), and the spread of values can be so small, especially when done with only a few evaluations.

When compared to the mean, the median can give some indication of the direction and degree of skew in the distribution. That is: if the median is above the average, the distribution favors higher values, and if the median is below the mean, more students answered the questions negatively, with lower scores.

Keep this idea of skew and center in mind when evaluating the spread of values.

Mode The most common answer found in the data set.

As a very simple example: if 1 person gave a professor an 'F', 2 people, a 'D', 4 people a 'C', 10 people a 'B' and 4 people an 'A', the mode would be a grade of 'B'. The scores are given as their numerical values, so 0 is an F and 4 is an A.

In the case of a tie, the higher 'grade' is picked.

Not extremely useful for any statistical purpose, but it does given an idea of what the majority of your peers thought of this professor in the various areas they were ranked in.
Standard Deviation Measures the spread of the values in a uniform distribution.

The numerical value given assumes the distribution of values is uniform (which it most likely isn't), and then calculates the deviation of values in the distribution from the center. Generally, the higher the number, the larger the range of grades students gave a particular professor.

The numerical value indicates what percentage of answers fall within a +/- range of it. About 68% of all answers will fall in between one standard deviation from the center, about 95% will fall in between two standard deviations, and about 99.7% will fall in between three standard deviations.

A simple example: if the center of a professor's grade is 3.2 with a standard deviation of 0.5, then about 68% of students rating this professor rated them in between a 2.7 and a 3.7; about 95% of them rated the professor somewhere in between a 2.2 and a 4.0 (would be a 4.2, but 4.0 is the highest rating).

The standard deviation is included to give some idea of the spread, but its use is flawed in a number of very serious ways. First of all, the concept of a standard deviation is based upon a uniform distribution, which these scores most certainly are not.

Secondly, standard deviations work with values that are a distance away from a center of a distribution of values. But what's our center in this data? Typically, the median is used as a center, but if the median and the mean don't match, then the distribution is skewed and the standard deviation is meaningless anyway. So, for our purposes, either the median or the mean could be used, but both are inherently incorrect, unless they're basically equal to each other. We recommend using the mean as a basis for the center value.

Finally, standard deviations work best on large sets of data with many varied possible values. That's not the case with here. Often times, data is based on a few evaluations, and there's a finite set of values that are possible in terms of rating a professor (the positive, real integers). This limits the standard deviation's effectiveness to accurately describe spread (we really should be using quartiles to describe spread, which we may add as a feature at some point).