Shape of a distribution
Two plots can share a center and a spread and still look nothing alike. How do you name the outline of a data set, and what does the outline tell you?
Where you are 3 inside
What this area is about
The first thing the eye takes from a dot plot or histogram is its outline. A few words cover most real data: symmetric, skewed to the left or right, uniform, bimodal. Naming the shape turns a picture into a sentence, often hints at where the data came from, and decides which center and spread are worth reporting.
How these fit together
Definitions. Symmetric and skewed distributions names a shape with one long tail after the side the tail runs to. Uniform and bimodal shapes names the flat shape and the two-humped one, which often means two groups were mixed.
A result. Mean, median and skew shows that a long tail pulls the mean toward it while the median stays with the bulk, so in skewed data the median is usually the better typical value, while the mean still serves when the total matters.
A path through it
Symmetric and skewed shapes first, then mean and median under skew. Uniform and bimodal shapes can come at any point.
Shape, center and spread together make up describing a distribution. Smoothing an outline into a curve leads to density curves and the most important symmetric shape of all, the normal distribution.