Guides

Longer explanations, for when the number itself is not the whole question.

Understanding standard deviation

• What is standard deviation?

  What the number means, its units, how to read high, low and zero, and why it is never negative.

• How to calculate standard deviation

  The six steps on real numbers, both formulas worked in full, common mistakes, and four practice problems.

• Standard deviation vs variance

  SD is the square root of variance: same information, different units. Formulas, a worked example, when to use each.

• The standard deviation formula

  Both formulas term by term, why deviations are squared, and why the shortcut formula fails on a computer.

• Symbols and notation

  σ versus s, μ versus x̄, and the Greek-for-population rule that makes the whole system predictable.

• Sample vs population

  The question that decides the denominator, and a table of how much it changes the answer at each n.

• Standard deviation vs standard error

  SD measures data spread; SE measures how precise your mean estimate is. Same formula, a different question.

In other tools

• Standard deviation in Excel

  STDEV.S, STDEV.P, conditional SD with IF, the text-stored-as-number trap, and Google Sheets differences.

• Standard deviation on a TI-84

  Exact keystrokes, reading Sx versus σx, frequency lists, and the errors that produce wrong answers.

• Standard deviation on a Casio

  Keystrokes for the fx-991CW, fx-991EX, fx-991ES PLUS, fx-83GT and fx-82MS families, sx versus σx, and frequency tables.

• Standard deviation in Python

  numpy.std, pandas .std() and statistics.stdev, and the ddof default that makes NumPy differ from Excel.

• Standard deviation in R

  sd() and var() are sample-only; the population SD, NA handling, by-group with dplyr, weighted and pooled.

In practice

• Standard deviation in psychology

  The definition, IQ and T-score scales, APA-style M and SD, and Cohen’s d from the SD.

• Standard deviation in finance

  Volatility, risk measurement, portfolio SD, Sharpe ratio, and value at risk: how SD became finance’s standard risk measure.

Written and reviewed by our editorial team. Last updated October 18, 2026. Method and sources: how these numbers are computed.