Introductory Statistics Calculators
Describe data, explore probability, estimate uncertainty and compare means.
Start with the question and the study design, then choose a calculation. These tools support introductory statistics in business, psychology, biology, social science and engineering.
Work from summaries and distributions to intervals, tests and simple regression. Record the sample size, variable units and sampling method before entering values. Use plots to check the shape of the data and residuals, rather than judging a model from one statistic.
These are selected course tools, not a complete statistical package. A small p-value does not establish causation, and a calculator cannot repair biased sampling.
Key Concepts
- •Compare center and spread before making an inference.
- •Translate an event into a probability and inspect a distribution.
- •Choose assumptions before calculating an interval or a test.
- •Read a slope in its units and inspect residuals.
Prerequisites
Algebra and proportions
Rearrange equations and interpret percentages.
Study design
Distinguish independent observations, paired data and populations from samples.
1. Describe the data
Compare center and spread before making an inference.
Mean, Median, Mode Calculator
Calculate the mean, median, and mode of a dataset from summary statistics. These three measures of central tendency describe where data clusters and are essential for any statistical analysis.
Standard Deviation Calculator
Calculate the standard deviation and variance of a dataset from summary statistics. Supports both population and sample standard deviation with Bessel's correction for unbiased estimation.
Interquartile Range (IQR) Calculator
Calculate the interquartile range and identify outlier boundaries using the 1.5*IQR rule. The IQR measures the spread of the middle 50% of data and is robust to extreme values.
2. Model probability
Translate an event into a probability and inspect a distribution.
Probability Calculator
Calculate the probability of single and combined events using fundamental probability rules. Covers union, intersection, and complement for independent and dependent events.
Normal Distribution Calculator
Compute P(X < x), P(X > x), P(a < X < b), z-scores, and inverse normal with an interactive bell curve
Bayes' Theorem Calculator
Calculate conditional probability using Bayes' theorem. Determine the posterior probability of a hypothesis given prior knowledge and new evidence from tests or observations.
3. Estimate and test
Choose assumptions before calculating an interval or a test.
Confidence Interval Calculator
Compute confidence intervals using z or t distribution with margin of error, SE, and visual interval bar
Hypothesis Testing Calculator
Step-by-step one-sample z-test, one-sample t-test, two-sample Welch t-test and paired-samples t-test, with effect sizes and a rejection region chart
4. Fit a relationship
Read a slope in its units and inspect residuals.