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Standard Deviation (Simplified) Calculator

Measure of the spread of scores around the mean.

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Std. Deviation

Formula first

Overview

The standard deviation is a fundamental measure of dispersion that quantifies the spread of data points around the mean. In psychological research, it indicates whether individual scores are tightly clustered or widely distributed across a scale.

Symbols

Variables

\sigma = Std. Deviation, SS = Sum of Squares, n = Count

Std. Deviation
Sum of Squares
Count

Apply it well

When To Use

When to use: This simplified population formula is used when the researcher has access to the entire group of interest rather than a sample. It assumes the data follows a normal distribution and is measured on an interval or ratio scale.

Why it matters: It allows psychologists to determine the reliability of their data and identify outliers within a dataset. Understanding the standard deviation is crucial for interpreting standardized test scores, such as IQ, where the mean and deviation define typical human performance.

Avoid these traps

Common Mistakes

  • Forgetting to square the differences.
  • Forgetting the square root at the end.

One free problem

Practice Problem

A psychologist measures the reaction times of 25 participants. The Sum of Squares (SS) for the group is calculated as 400. Calculate the standard deviation (SD) for this population.

Sum of Squares400
Count25

Solve for:

Hint: Divide the Sum of Squares by the number of participants, then take the square root of the result.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Wikipedia: Standard deviation
  2. Britannica: Standard deviation
  3. Statistics for Psychology by Arthur Aron, Elaine Aron, Elliot Coups
  4. Discovering Statistics Using IBM SPSS Statistics by Andy Field
  5. Statistics for Psychology by Arthur Aron, Elaine Aron, and Elliot Coups
  6. Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). Sage Publications.
  7. Aron, A., Aron, E. N., & Coups, E. J. (2013). Statistics for Psychology (6th ed.). Pearson Education.
  8. GCSE Psychology / Mathematics — Statistics