01
Observe
Define units, variables, measurement, sampling, and the process that generated the data.
Data · variability · probability · inference
Statistics
Statistics studies how data vary, how samples relate to larger populations or processes, and how uncertainty changes what conclusions are justified. The subject links measurement, description, probability models, estimation, prediction, and inference.
Statistical workflow
A number becomes evidence only after you understand how it was produced.
Good statistical reasoning moves back and forth among data, design, probability, and interpretation. Calculation is one piece of the pipeline, not the pipeline itself.
02
Describe
Summarize distributions with center, spread, shape, relationships, and visual displays.
03
Model
Represent randomness and uncertainty with probability models and assumptions.
04
Infer
Use sample information to estimate, compare, predict, or update claims while keeping uncertainty visible.
Variability is signal about the process
The same population can produce many different samples.
Sampling distributions describe how a statistic varies across hypothetical repeated samples. They are the bridge between one observed statistic and uncertainty about the process that generated it.
standard error ≈ typical sample-to-sample variation in a statistic
Sampling-distribution lab
Repeatedly sample from a strongly right-skewed population and watch the distribution of sample means change.
Source populationindividual observations · right-skewed
0value / mean4.5
Sample means600 means · sample size n = 5
0value / mean4.5
Observations per samplen = 5
Least-squares regression
x predictorclick anywhere to add a pointy response