Standard Deviation Calculator
Measure how spread out values are around the mean.
Formula: √(Σ(x − mean)² ÷ n)Phase 10.2
Statistics Intelligence
Statistics calculators for spread, probability, samples, distributions, confidence intervals, regression, research planning, and random generation. Each tool explains the formula and what the result means.
Statistics cluster standard
Phase 10.2 calculators are designed for educational use. They help learners understand formulas, avoid common interpretation mistakes, and move from a statistical result to a sensible next learning step.
Statistics calculators included
Variance Calculator
Measure average squared distance from the mean.
Formula: Σ(x − mean)² ÷ nProbability Calculator
Estimate the chance of an event as a percent.
Formula: Favorable outcomes ÷ Total outcomesPermutation Calculator
Count ordered arrangements when order matters.
Formula: n! ÷ (n − r)!Combination Calculator
Count selections when order does not matter.
Formula: n! ÷ (r! × (n − r)!)Z-Score Calculator
Find how many standard deviations a value is from the mean.
Formula: (x − mean) ÷ standard deviationConfidence Interval Calculator
Estimate a range around a sample mean.
Formula: Mean ± z × (SD ÷ √n)Correlation Calculator
Measure the strength and direction of a linear relationship.
Formula: Pearson rRegression Calculator
Estimate a simple linear trend line from paired values.
Formula: y = mx + bSample Size Calculator
Estimate how many responses are needed for a basic proportion study.
Formula: (z² × p × (1 − p)) ÷ e²Margin of Error Calculator
Estimate uncertainty for a sample proportion.
Formula: z × √(p(1 − p) ÷ n)Normal Distribution Calculator
Place a value inside a normal distribution.
Formula: z = (x − μ) ÷ σBinomial Distribution Calculator
Estimate probability of a number of successes across repeated trials.
Formula: C(n,k) × p^k × (1 − p)^(n − k)Chi-Square Calculator
Compare observed counts with expected counts.
Formula: Σ((Observed − Expected)² ÷ Expected)T-Test Calculator
Estimate a two-sample t statistic for comparing means.
Formula: (Mean1 − Mean2) ÷ √(s1²/n1 + s2²/n2)P-Value Calculator
Estimate a rough two-tailed p-value from a z-like statistic.
Formula: Approximation from z-scoreRandom Number Generator
Generate a random whole number in a chosen range.
Formula: Random integer between min and maxRandom List Generator
Generate a list of random whole numbers.
Formula: Random integers between min and maxQuartile Calculator
Split a data set into lower, middle, and upper quarters.
Formula: Q1, Q2, Q3 from sorted valuesPercentile Calculator
Find a value at a selected percentile in a sorted data set.
Formula: Rank position = p ÷ 100 × (n − 1)How to use this cluster
- Choose the statistical method closest to your data question.
- Enter clean numeric values using commas or spaces for lists.
- Review the formula and the learning note before using the result.
- Use related calculators when you need a second step such as variance before standard deviation or sample size before margin of error.