Browser-first · No sign-up

Standard Deviation Calculator – Full Descriptive Stats

Compute population/sample standard deviation, variance, mean/median/mode, quartiles, IQR, z-scores, outliers, frequency tables, and a histogram — all client-side.

No uploads. Everything runs locally in your browser.

Status

Example loaded. Click Calculate to get stats.

Total numbers: 8Valid numbers: 8Min: 12Max: 35Mode: compare
Quick insights
  • Outliers: None
  • Distribution: Moderate spread, Slight right skew
  • Coefficient of variation (pop): 31.52
  • Coefficient of variation (sample): 33.69
Summary
Mean: 22.38
Median: 21
Mode: 20
Min / Max: 12 / 35
Range: 23
Variance (pop): 49.73
Variance (sample): 56.84
SD (pop): 7.05
SD (sample): 7.54
Standard error (sample): 2.67
Quartiles & outliers
Q1: 17.5
Q2 (Median): 21
Q3: 27.5
IQR: 10
Outliers (IQR rule): None
Deviation table
ValueDeviationSquaredZ (pop)
12-10.37107.64-1.47
15-7.3754.39-1.05
20-2.375.64-0.34
20-2.375.64-0.34
22-0.370.14-0.05
252.636.890.37
307.6358.141.08
3512.63159.391.79
Frequency table
ValueCount
121
151
202
221
251
301
351
Histogram (preview)
12
19.67
19.67
27.33
27.33
35
Explanation

Population variance = Σ(x - mean)² / N. Sample variance = Σ(x - mean)² / (N - 1). SD is the square root of variance.

Coefficient of variation = (SD / mean) × 100. Standard error = sample SD / √n.

Outliers use IQR rule: bounds = Q1 - 1.5×IQR and Q3 + 1.5×IQR.

What is this tool

The Standard Deviation Calculator is a full descriptive statistics helper. It compares population vs sample results, shows variance, mean/median/mode, quartiles/IQR, z-scores, frequency tables, deviation tables, outliers, and a histogram preview. With copy-ready outputs and invalid-token handling, you can check classroom grades, finance volatility, survey data, or QC samples quickly and privately in your browser.

Educational extras like coefficient of variation, standard error, and distribution insights make it useful for studying or validating manual calculations. Outlier detection via the IQR rule and z-score previews help spot anomalies before deeper analysis.

Use cases

  • Summarize classroom grades with mean, SD, and outliers flagged.
  • Check business/finance data for volatility and dispersion.
  • Analyze survey responses with frequency and deviation tables.
  • Verify QC or manufacturing measurements for spread and outliers.
  • Compare population vs sample statistics for assignments or reports.

These scenarios show up in exam prep, analytics, dashboards, and quick code/data reviews. Transparent steps reduce mistakes and keep teams aligned on the math.

Popular ways to use this tool

  • Paste data from spreadsheets and instantly get SD, variance, and outliers.
  • Share deviation/frequency tables in homework or sprint tickets.
  • Use precision toggle for cleaner presentations vs detailed analysis.
  • Benchmark datasets: compare sample vs population SD in one view.
  • Spot distribution shape with histogram and mean vs median skew hints.

Copyable summaries and tables let you move results into docs, chats, or LMS submissions without recalculating. The calculator keeps descriptive stats fast, visual, and trustworthy.

How to use Standard Deviation Calculator

  1. Paste numbers separated by commas, spaces, tabs, or new lines.
  2. Choose Population, Sample, or Compare Both; set decimal precision if needed.
  3. Click Calculate to see SD/variance, mean/median/mode, quartiles/IQR, outliers, and tables.
  4. Copy summary, deviation table, or frequency table; use Fill example or Clear to reset.

Key features of Standard Deviation Calculator

  • Population and sample standard deviation side-by-side (Compare mode)
  • Variance, mean/median/mode, range, quartiles, IQR, z-scores, coefficient of variation, standard error
  • Deviation table, frequency table, outlier detection via IQR, and histogram preview
  • Handles decimals, negatives, repeated values, and mixed delimiters with invalid token warnings
  • Copy outputs, example fill, precision selector, and responsive two-column layout

Standard Deviation Calculator — key benefits

  • Completely free with no signup or registration required.
  • Runs entirely in your browser — your data is never uploaded.
  • Works on desktop, tablet, and mobile devices.
  • Instant results with no waiting or processing queues.
  • Part of the ToolCircuit suite of free online math tools tools.

FAQ

Do you support both population and sample SD?

Yes. Choose Population, Sample, or Compare to see both side by side (sample uses N-1).

How are outliers detected?

Using the IQR rule: values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR are flagged as outliers.

Can I copy the tables?

Yes. You can copy the summary, deviation table, and frequency table with the provided buttons.

Do you upload my data?

No. All calculations run locally in your browser.

Is this statistics calculator free?

Yes. It’s free, fast, and requires no login.

Related tools