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Statistics

Choose the path that matches your task: summarize a data set, calculate a probability, interpret a z-score, practice a skill, or check a formula.

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  1. Summarize Summarize a data set Find measures of center and spread while keeping sample and population quantities clearly labeled.
  2. Calculate Calculate one focused result Work with standard deviation, event probability, or a z-score using the inputs required by that calculation.
  3. Practise Practice statistical reasoning Use a visible worked sample to connect a calculation with its interpretation and review plan.
  4. Reference Look up a formula Scan formulas by topic, confirm every symbol and condition, then follow a worked application.

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.

Resource directory

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Solvers and calculators

Learning guides

Practice

Formula references

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. 1
    Describe one variable

    Sort a small data set and calculate its center and spread before interpreting what those values say.

  2. 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. 3
    Build probability models

    Define the sample space and events before choosing an addition, multiplication, complement, or conditional rule.

  4. 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.

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Created by Mathos AI. Methods, conditions, and checks are shown so you can review the mathematical reasoning.