A Distribution Is a Shape

Values have patterns, not just averages

A distribution describes which values occur and how often. A symmetric distribution has comparable shape on either side of its center. A skewed distribution has a longer tail on one side. A multimodal distribution has multiple peaks, often revealing that several different subpopulations were mixed together.

request count
  ^       ###
  |     #######           ##
  |   ###########       ####
  +----------------------------> latency
      normal traffic       timeouts

The bell-shaped normal distribution is useful because many measurement errors and aggregate quantities approximate it, but real ML features do not owe us a bell curve. Income, file size, response time, and event frequency commonly have long right tails. Plot or summarize the actual shape before selecting transformations or thresholds.

Analogy: Saying a city has an average elevation tells you little about whether it is a flat plain, a valley beside a mountain, or two islands. A distribution is the terrain map.

Tip: Histograms show counts in value ranges; density plots smooth that view; box plots compactly show median, quartiles, and candidate outliers. Use more than one view when stakes are high.