Center and spread
A data set is a list of different numbers. Which single number says where it sits, which says how far it wanders, and how do you choose between them?
Where you are 13 inside
What this area is about
A list of numbers is summarized by a center (a typical value) and a spread (how far values wander from it). The right pair depends on the data’s shape and on whether a few extreme values should count.
How these fit together
Centers. The mean is a fair share and a balance point; the median and mode need no adding.
Spreads. Range and IQR cut sorted data at fixed places. Mean absolute deviation averages distances from the mean, and standard deviation squares them first.
Extreme values. The 1.5 IQR rule is the procedure that flags outliers, and resistant measures is the result that says which summaries one extreme value drags along.
Describing and comparing. Shape names the outline, describing a distribution puts shape, center and spread into sentences, then comparing two distributions and the gap between means in MADs set two groups side by side.
Changing scale. Shifting and rescaling says how \bar{x} and s move, and standardizing puts any data set whose values are not all equal on a scale with mean 0 and standard deviation 1.
A path through it
Mean and median and mode come first, in either order. Range and IQR follow the median, then the 1.5 IQR rule, resistant measures, and shape. MAD can come any time after the mean; standard deviation needs MAD and resistant measures, then shifting, then standardizing. Shape leads to describing, then comparing two distributions, then comparing in MADs, which also needs MAD.
Next come box plots, correlation and the normal distribution.