Most people have been introduced to the concept of "average", and many use it with the assumption that there is only one average. Others think there are only three. In actual fact, there are many, but the three most common are described below: the mode, the median and the arithmetic mean.


Mode:
The "mode" is simply the point in a distribution with the greatest frequency. In other words, it is the most commonplace value of the variable in question.

Example:
For a single deck, (ie. 2s = 2, 3s = 3, etc., Face Cards = 10, and Aces = either 1 or 11), the mode is 10, because there are 16 ten valued cards and there are only 4 each of the other values.

Median:
The "median" is the middle value of the data. Imagine that we arrange our data from the lowest value to the highest value like attaching a value onto a "Cheerio" and then hanging each "Cheerio" on a big long string. Now, after they've all been strung, we simultaneously eat one "Cheerio" from each end. Eventually, when we get to the middle, we have one (sometimes two) Cheerios left. If we have one Cheerio left, then we read the value attached to it. This value is the median. If there are two "Cheerios" left, to find the median we take the arithmetic mean of the values attached to these two remaining Cheerios :-)

Quiz:
For a single deck, (ie. 2s = 2, 3s = 3, etc., Face Cards = 10, and let Aces = 1), "What is the median?

Hint: If you have trouble figuring this out, arrange a single deck from Aces through Kings, like so A A A A 2 2 2 2 3 3 3 3 . . . Q Q Q Q K K K K. Then simultaneously take one card off each end until you get to the last two cards. The arithmetic mean of the last two cards is the median.

Arithmetic Mean:
The arithmetic "mean" is the simple average value of the data. If there are "n" values: X1, X2, . . ., Xn
then the mean is the sum of these values, divided by "n":

mean = (X1 + X2 + X3 + . . . + Xn) / n

Quiz:
For a single deck, (ie. 2s = 2, 3s = 3, etc., Face Cards = 10, and let Aces = 1), "What is the mean?"