Statistics turns data into useful descriptions and carefully bounded conclusions. Start with the statistics calculator for a numerical summary, use a focused calculator when the model is already known, or review the formulas and reasoning before you calculate.
Concept map
Ideas that organize this subject
Data and variables
Identify what each observation measures, whether a variable is categorical or quantitative, and which population the data are meant to describe.
Center and spread
Use mean, median, mode, range, interquartile range, variance, and standard deviation to describe different features of a distribution.
Events and probability
Model outcomes with a sample space, then distinguish complements, unions, intersections, independence, and conditional probability.
Standardized scores
Use a z-score to express a raw value as a signed number of standard deviations from its reference mean.
Sample and population
A parameter describes a population. A statistic is calculated from a sample and may be used to estimate a population parameter.
Suggested order
A practical learning sequence
1
Describe one variable
Sort a small data set and calculate its center and spread before interpreting what those values say.
2
Choose sample or population notation
Decide whether the listed observations are the entire group of interest or a sample from a larger population.
3
Build probability models
Define the sample space and events before choosing an addition, multiplication, complement, or conditional rule.
4
Standardize measurements
Compare values on different scales by subtracting the appropriate mean and dividing by the appropriate standard deviation.
Common questions
Statistics FAQ
What should I study first in statistics?
Begin with data types, populations and samples, then learn measures of center and spread. Probability and standardized scores are easier to interpret once those foundations are clear.
Is statistics the same as probability?
No. Probability starts with a model and reasons about possible outcomes. Statistics starts with observed data and describes the data or uses them to learn about a wider population.
Why do sample and population formulas differ?
They answer different questions. A population formula describes every member of the group of interest. A sample formula uses observed data to estimate an unknown population quantity, which changes the variance denominator from n to n minus 1.
Where should I check notation and formula conditions?
Use the statistics formula sheet. It defines the symbols, separates sample and population notation, and states restrictions such as a positive standard deviation or a nonzero conditioning probability.
Continue learning
Useful next steps
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