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statistics

A statistics calculator computes summary statistics from a list of numbers — mean (average), median (middle value), mode (most frequent), range (max − min), variance, standard deviation, quartiles (Q1, Q2, Q3), interquartile range, and selected percentiles. The ZTools Statistics Calculator accepts any list (one number per line, comma-separated, or space-separated), runs all computations in the browser, and shows results with a small distribution chart. No upload, no signup, no row limit.

Use cases​

Quick descriptive stats for a survey​

A 200-row response column. Paste, get mean / median / SD / quartiles instantly — faster than opening Excel for one column.

Compare two datasets​

Stats side by side reveal which has higher central tendency, which is more spread out. Calculator runs both and tabulates.

Spot outliers​

Values more than 1.5 × IQR beyond Q1 / Q3 are conventional outliers. Calculator flags them.

Verify a textbook problem​

Homework gives a list; you computed mean = 14.5. Calculator confirms or contradicts. Useful for self-checking.

How it works​

  1. Paste numbers — One per line, comma-separated, or space-separated. Tool detects automatically.
  2. Pick population vs sample — Variance and SD differ for a population (divide by n) vs a sample (divide by n−1, Bessel's correction). Default: sample.
  3. Configure precision — Decimals to display (default 4). Bigger numbers get scientific notation automatically.
  4. Read results — Table of statistics + a small histogram showing distribution shape.

Examples​

Input: [1, 2, 3, 4, 5]

Output: Mean: 3. Median: 3. Mode: none (all unique). Range: 4. Sample SD: 1.5811. Q1: 2. Q3: 4. IQR: 2.

Input: [10, 20, 20, 30, 40, 100]

Output: Mean: 36.67 (skewed by 100). Median: 25 (more representative). Mode: 20. SD: 31.85. The mean-vs-median gap signals skew.

Input: Outlier detection

Output: Q1 = 20, Q3 = 40, IQR = 20. Outlier threshold: > 70 or < −10. Value 100 flagged as outlier.

Frequently asked questions​

Sample SD vs population SD?

Sample SD divides by n−1 (Bessel's correction) — gives an unbiased estimate of the population SD. Population SD divides by n — exact when you have all the data. Default is sample (more common in practice).

Mean vs median — which to report?

Mean is sensitive to outliers; median isn't. For income, house prices, response times — report median. For symmetric distributions, mean and median are similar; either works.

How is the median calculated for even count?

Average of the two middle values. For [1,2,3,4], median = (2+3)/2 = 2.5.

How is mode reported when multiple modes exist?

All values tied for highest frequency. If everything is unique, "no mode" is reported. Multimodal distributions get a list.

Privacy?

All computation in the browser. Numbers never uploaded.

Maximum list size?

Practical limit is browser memory — millions of values work fine. Quartile computation is O(n log n) (sort).

Tips​

  • When mean and median diverge significantly, the data is skewed — investigate the tail.
  • Always include sample size (n) when reporting any of these stats — without n, they're hard to interpret.
  • For inference (significance tests, confidence intervals), use a dedicated tool — descriptive stats only describe; they don't test hypotheses.
  • Outlier detection at 1.5 × IQR is a convention, not a rule. For strict outliers, use 3 × IQR or domain-specific thresholds.

Try it now​

The full statistics runs in your browser at https://ztools.zaions.com/statistics — no signup, no upload, no data leaves your device.

Open the tool ↗

Last updated: 2026-05-06 · Author: Ahsan Mahmood · Edit this page on GitHub