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  4. Statistics Calculator

Statistics Calculator

Arithmetic and geometric means, σ and s, variance, quartiles, IQR, and Σx / Σx² from a comma-separated list.

Statistics

  • Average Calculator
  • Mean, Median, Mode, Range Calculator
  • Statistics Calculator
  • Standard Deviation Calculator
  • Number Sequence Calculator
  • Probability Calculator
  • Permutation and Combination Calculator
  • Sample Size Calculator
  • Z-score Calculator
  • Confidence Interval Calculator
  • P-value Calculator

How it works

Summarize a data set with central tendency and spread. Population divides by n; sample divides by n−1. Variance is std dev squared.

x̄ · GM · σ/s · σ²/s² · Q1 Q3 IQR

When to use

Use this tool when you need to: try 10, 2, 38, 23, 38, 23, 21, 23 — mean 22.25, GM ≈17.12, σ ≈11.51, s ≈12.30. Non-positive data leaves GM undefined.

How to use this tool

  1. Enter your values in the fields above.
  2. Review the formula and any mode options for your problem.
  3. Read the result and the step-by-step solution.

Try 10, 2, 38, 23, 38, 23, 21, 23 — mean 22.25, GM ≈17.12, σ ≈11.51, s ≈12.30. Non-positive data leaves GM undefined.

Frequently asked questions

What is the Statistics Calculator?
Summarize a data set with central tendency and spread. Population divides by n; sample divides by n−1. Variance is std dev squared.
How do I use the Statistics Calculator?
Enter the required values, then calculate. The Statistics Calculator shows results, formulas, and step-by-step work when available. No account is required.
What formula does the Statistics Calculator use?
x̄ · GM · σ/s · σ²/s² · Q1 Q3 IQR

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Statistics calculator

Add numbers one at a time with the keypad, or paste a list under Comma list. Same calculation either way.

Entry mode

n = 00

Type digits, then press ADD to save that number. Stat keys (x̄, σ, s, GM…) put that result on the screen.

Added values

Empty — press ADD after typing a number.

CAD clears the whole list. C clears only the entry on the screen.

Try an example

How it works

What this calculator reports

A generalized statistics summary: arithmetic mean, geometric mean, median, mode, population and sample standard deviation and variance, range, quartiles, IQR, and the raw sums Σx and Σx² plus the sum of squared deviations. Visit the dedicated Mean/Median/Mode/Range or Standard Deviation calculators for deeper examples of those pieces alone.

Two ways to enter data

Switch entry mode with the tabs. Keypad works like a handheld stats calculator: enter each value and press ADD; stat keys (x-bar, sigma, s, GM…) show that measure on the display. Comma list is for pasting bulk data — press Calculate for the full tile summary. The data set is shared between tabs.

Geometric mean

The geometric mean multiplies the values and takes the nth root — equivalently exp of the average of the natural logs. It is useful when averaging ratios or quantities on very different scales so no one range dominates (unlike the arithmetic mean). Example data 1, 5, 7, 9, 12 uses GM = (1·5·7·9·12)^(1/5). Any zero or negative value makes GM undefined for real numbers.

σ vs s and variance

Population standard deviation σ divides the sum of squared deviations by n; sample standard deviation s divides by n−1 (Bessel’s correction). Variance is not listed as a separate button on some tools because it is simply the standard deviation squared (σ² or s²) — this calculator reports both forms explicitly so you do not have to square by hand.

Quartiles and IQR

Q1 and Q3 approximate the 25th and 75th percentiles of the ordered list. The interquartile range IQR = Q3 − Q1 measures the middle 50% of the data and is more robust to outliers than the full range.

Related calculators

Descriptive stats tools share the same data-entry style. Average focuses on the mean alone; sequences generate ordered lists instead of summarizing a sample.

  • Mean, Median, Mode, Range Calculator
  • Standard Deviation Calculator
  • Sample Size Calculator
  • Probability Calculator
  • Number Sequence Calculator
  • Average Calculator