When should I use median instead of mean?

Use the median when your data has outliers or is heavily skewed. The mean (arithmetic average) is sensitive to extreme values — one billionaire in a sample of 100 people will skew the mean income drastically, but the median is unaffected. Income, house prices and reaction times all typically use median because the distributions are skewed. Use mean when data is symmetric and roughly normal.

What is the difference between population and sample standard deviation?

Population standard deviation (σ) divides by N (the population size). Sample standard deviation (s) divides by N−1 (Bessel's correction) because a sample tends to underestimate variability. So for a sample of 30 measurements with sum of squared deviations 145: sample SD = √(145/29) = 2.24, population SD = √(145/30) = 2.20. Use sample SD unless you have data on the entire population.

How do I calculate a 95% confidence interval?

For a sample mean: CI = mean ± (1.96 × SE), where SE = standard deviation ÷ √n. So if mean = 50, SD = 10, n = 100, then SE = 1, and the 95% CI is 48.04 to 51.96. The 1.96 is the z-critical value for 95% — use 1.645 for 90%, 2.576 for 99%. For small samples (n < 30) use t-distribution critical values.

What is a z-score and how do I interpret it?

A z-score tells you how many standard deviations a value is from the mean. Formula: z = (x − mean) / SD. A z-score of 0 means the value equals the mean; +1 means 1 SD above; −2 means 2 SDs below. About 68% of normal data falls within ±1 SD, 95% within ±2 SDs, 99.7% within ±3 SDs (the 68-95-99.7 rule). Z-scores above ±3 are usually outliers worth investigating.

What sample size do I need for a 95% confidence interval?

Sample size depends on the margin of error you'll accept and the variability in the population. Quick formula for a proportion: n = (1.96/E)² × p(1−p), where E is margin of error and p is the expected proportion. For p = 0.5 (most conservative) and E = 0.05: n ≈ 384. So 384 people gives you ±5% accuracy on opinion polls at 95% confidence.

Statistics Tools

Q: What is a z-score and how do I interpret it?

A z-score tells you how many standard deviations a value is from the mean. Formula: z = (x − mean) / SD. A z-score of 0 means the value equals the mean; +1 means 1 SD above; −2 means 2 SDs below. About 68% of normal data falls within ±1 SD, 95% within ±2 SDs, 99.7% within ±3 SDs (the 68-95-99.7 rule). Z-scores above ±3 are usually outliers worth investigating.

Q: What sample size do I need for a 95% confidence interval?

Sample size depends on the margin of error you'll accept and the variability in the population. Quick formula for a proportion: n = (1.96/E)² × p(1−p), where E is margin of error and p is the expected proportion. For p = 0.5 (most conservative) and E = 0.05: n ≈ 384. So 384 people gives you ±5% accuracy on opinion polls at 95% confidence.

Explore free statistics calculators to solve statistical problems quickly and accurately without complicated manual calculations. Our online statistics calculator helps students, researchers, teachers, and professionals perform essential statistical calculations, including mean, median, mode, standard deviation, variance, probability, and correlation. These easy-to-use tools simplify data analysis, save time, and help you understand statistical results for academic research, assignments, and everyday analytical tasks.

Editorially reviewed Reviewed by Agarapu Ramesh, science educator (chemistry). LinkedIn

Last reviewed: May 2026 | Standard statistical formulas

Choose a calculator for formulas, live results, charts, examples, FAQ, glossary and references.

Mean Median Mode Calculator
Mean median mode calculator for central tendency, range, quartiles, variance and standard deviation with live chart, formulas and steps.
Weighted Average Calculator
Weighted average calculator for values and weights with steps, formula, and a clear explanation of what a weighted average means.
Standard Deviation Calculator
Standard deviation calculator for sample and population SD with variance, mean, deviations, formulas, chart and step-by-step working.
Variance Calculator
Variance calculator for sample s squared and population sigma squared with coefficient of variation, formula, chart and steps.
Z Score Calculator
Z score calculator for z=(x-mu)/sigma, percentile from normal CDF, reverse x from z, formula and bell curve.
P Value Calculator
P value calculator from Z, t, chi-square and F statistics with one-tailed and two-tailed results, formulas and interpretation.
T Test Calculator
T test calculator for one-sample, Welch two-sample and paired tests with t statistic, df, p-value, effect size and steps.
Confidence Interval Calculator
Confidence interval calculator for means and proportions using z or t critical values, margin of error, formula and steps.
Probability Calculator
Probability calculator for union, intersection, conditional probability, complement and normal CDF with formulas and Venn chart.
Sample Size Calculator
Sample size calculator for means and proportions with confidence level, margin of error and finite population correction.
Combination Permutation Calculator
Combination permutation calculator for nCr, nPr, repetition formulas and factorials using BigInt for large exact integers.
Chi Square Calculator
Chi square calculator for goodness-of-fit and contingency table independence tests with p-value, df and steps.
Correlation Coefficient Calculator
Correlation coefficient calculator for Pearson r, Spearman rho, t test, p-value, strength interpretation and scatter plot.
Linear Regression Calculator
Linear regression calculator for simple OLS best-fit line, slope, intercept, R squared, prediction and scatter plot.
Margin Of Error Calculator
Margin of error calculator for means and proportions with confidence level, z critical value, formula and interpretation.
Five Number Summary Calculator
Five number summary calculator for min, Q1, median, Q3, max, IQR, fences, outliers and live box plot.

What these statistics tools do

The statistics tools help calculate descriptive statistics, probability, confidence intervals, hypothesis tests, regression, correlation, combinations, permutations, and sample-size estimates. Each tool shows the formula and a worked interpretation so the result is easier to verify.

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What this collection does

This page groups related statistics tools so visitors can choose the right calculator or converter without guessing from a filename alone. The links, summaries, and supporting notes explain what each page is for and what kind of input it expects.

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Start with the tool that matches the measurement, tax topic, network task, or text operation you need.
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Frequently Asked Questions

Is Statistics Tools free to use?

Yes, Statistics Tools is completely free with no signup required. It runs entirely in your browser, so you can use it as often as you need.

How accurate is Statistics Tools?

Statistics Tools uses standard, well-established formulas to provide accurate educational results. For complex or critical decisions, consult a qualified professional.

Is my data private?

Yes. All calculations happen locally in your browser. Your inputs are not uploaded, logged, or stored on our servers.

Does Statistics Tools work on mobile?

Yes, Statistics Tools is fully responsive and works on phones, tablets, and desktop browsers without any installation.

Which statistics calculator should I start with?

Start with descriptive tools such as mean, median, standard deviation, or five-number summary when exploring data. Move to confidence intervals, p-values, regression, or chi-square only after the question and assumptions are clear.

How does an online probability calculator help calculate the chances of an event?

An online probability calculator helps determine the likelihood of an event occurring based on known outcomes and available data. It simplifies probability calculations for single events, multiple events, and independent or dependent outcomes, making it useful for students, researchers, and professionals working with statistics and data analysis.

How does a sample size calculator help determine the required number of participants for a study?

A sample size calculator estimates how many participants or observations are needed for a reliable research study based on factors such as population size, confidence level, margin of error, and expected response distribution. It helps researchers plan surveys, experiments, and statistical studies while improving the reliability of their findings.