Median and mode
The mean is not the only way to say what is typical. What other numbers can stand for a whole data set, and when are they the better choice?
Where you are 2 inside
What this area is about
Two more answers to “what is typical?” need no adding at all. The median is the middle value once the data are in order. The mode is the value that occurs most often. The median ignores how far the extreme values sit, and the mode works even for categories, like colors, that cannot be added or ordered.
How these fit together
A procedure. Finding the median sorts the data and takes the middle value; with an even number of values, two share the middle and the median is halfway between them. For n values the middle sits at position \displaystyle \frac{n+1}{2}.
A definition. Mode and bimodal data defines the most common value, and says what it means when two separate values are both common: often, two groups mixed together.
A path through it
The two can be taken in either order. The median comes first here because it is the one the rest of the branch builds on.
The median is the first cut of the quartiles, which lead to the interquartile range and box plots. Two-peaked data return in uniform and bimodal shapes, part of describing the shape of a distribution.