Any number used to represent many observations of a single variable or that
relates several variables together
Average
A statistic that is intended to provide a measure of what a ”typical” data point
is for a single variable
Mean
An average computed by adding all the observations of a variable together and
then dividing by the number of observations. In symbols, the mean of the data xi is
x = ∑xi∕n. This is more properly called the arithmetic mean. Most software, like
Excel, uses AVERAGE for the mean, which is the most commonly used average, and
it is the most robust average (it will change the least under repeated sampling of the
population)
Median
An average computed by first ordering the observations from smallest to largest
and then finding the number that splits the observations in half. Observe that this
number may or may not be a data point, depending on whether there are an even
or odd number of observations. 50% of the observations are less than or equal to the
median and 50% are greater than or equal to the median. If there are an even number
of points, the median is in between the two center numbers (see example 2)
Mode
An average computed by determining which observation(s) is repeated most often
(or most frequently). The mode is not necessarily unique, nor is it guaranteed to even
exist. This is really only useful for discrete numerical data with a few possible values
or for categorical data