Statistics foundations packet
Start with center and quartiles, calculate spread, then compare positions with z-scores.
Edit this packet →Read the data. Explain the result.
Statistics worksheets
Start with summaries and relationships, then use probability models to estimate parameters and evaluate evidence. Choose a focused worksheet or prepare a sequence through Bayesian updating, tests, intervals and regression.
32 printable resources, from reference sheets to configurable practice with worked answers.
Choose a worksheetChoose a starting point
Begin with averages, fractions, square roots and coordinate graphs. Use secure algebra before rearranging a z-score or fitting a regression line. For college inference, review probability models, functions and basic calculus. These are readiness suggestions; course order varies by school.
The convention changes the denominator
For the data 2, 4, 6, how much variation is there?
Mean 4; squared deviations total 8. Population variance is 8/3; sample variance is 8/2 = 4.
Divide by 3 if these are all the observations in the population. Divide by 2 when estimating population variance from this sample. Standard deviation is the square root of the corresponding variance.
Prepare a statistics worksheet packet
Start with a suggested sequence, then remove or reorder complete worksheets. Choose Letter or A4 and a student or teacher edition.
Statistics progression packet
Move through standard deviation, standard scores and normal models before studying correlation and regression.
Edit this packet →Statistics review packet
Collect six complete worksheets for revision, with separate worked answer pages in the teacher edition.
Edit this packet →Likelihood and Bayesian updating packet
Connect parameters, likelihood, discrete updates and posterior prediction.
Edit this packet →Priors and posterior uncertainty packet
Work through continuous priors, beta and normal updates, sensitivity and credible intervals.
Edit this packet →Hypothesis testing packet
Choose a test design, calculate evidence and interpret the conclusion across common data types.
Edit this packet →Intervals and bootstrap packet
Compare normal-model, large-sample and bootstrap uncertainty calculations.
Edit this packet →Regression models packet
Extend straight-line fitting to transformed curves, diagnostics and multiple predictors.
Edit this packet →Step 1
Describe the center and shape
Keep the observations and units visible. Compare a mean with a median, then use quartiles and box plots to describe spread without assuming a normal model.
Mean, median, mode & range
Mean, median, mode and range reference
Print a reference that explains mean, median, mode and range with worked examples. Compare odd and even datasets, negative values, tied modes and data with no mode.
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Mean, median, mode & range
Mean, median, mode and range practice
Generate ten datasets for mean, median, mode and range practice. Choose the requested statistics, observations per dataset, number range and signs, with separate answer pages.
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Graph
Five-number summaries
Calculate minimum, lower quartile, median, upper quartile and maximum for four or six datasets with 9–13 observations.
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Graph
Draw box-and-whisker plots
Find five-number summaries for three datasets, then draw each box plot on its labeled axis. Choose data lengths, order and number range.
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Measure variation
Decide whether the observations are the whole population or a sample. Show squared deviations, choose n or n - 1, then take the square root to restore the original units.
Statistics
Variance and Standard Deviation worksheets
Calculate population and sample spread from small data sets with explicit n and n - 1 denominators, units, and final rounding.
Preview and downloadStep 3
Standardize and use a normal model
A z-score describes distance from the mean in standard-deviation units. Converting that score to a normal probability requires an explicitly stated normal model.
Statistics
Z-Scores worksheets
Calculate z-scores, recover original values, and compare relative positions across data sets with positive standard deviations.
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Statistics
Normal Distribution worksheets
Standardize normal values, find below, above, and between probabilities, and invert the model for percentiles and central intervals.
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Investigate paired observations
Inspect the plot before describing a linear association. Fit a least-squares line, compare observed and predicted values, and explain why a trend alone does not establish a cause.
Statistics
Scatterplots and Correlation worksheets
Construct and read labeled scatterplots from actual paired observations, calculate Pearson r, and interpret linear association without claiming causation.
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Statistics
Linear Regression and Residuals worksheets
Fit ordinary least-squares lines with intercepts, predict responses, calculate observed-minus-predicted residuals, and identify extrapolation.
Preview and downloadStep 5
Connect data summaries to probability
Compare averages from observed data with probability-weighted expectations. Use a binomial model only when its fixed-trial, independence and constant-probability assumptions apply.
Probability
Discrete Probability Distributions worksheets
Use valid finite probability tables to find missing entries, event probabilities, expected value, and population variance.
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Probability
Binomial Distribution worksheets
Calculate exact, at-most, and at-least binomial probabilities plus mean and variance for bounded trial counts.
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Identify the inference problem
Separate observations and sample statistics from unknown population parameters. State what the data can describe and what requires an inferential model.
Statistics
Parameters, Statistics, and Inference worksheets
Classify study stages, identify observations and parameters, reject invalid statistics, and compute sample summaries.
Preview and downloadStep 7
Use likelihood and Bayesian updating
State a parameter model, compare likelihoods and update prior information. Keep evidence, posterior density, predictive probability and prior sensitivity distinct.
Statistics
Likelihood and MLE worksheets
Write and compare likelihoods, find bounded analytic MLEs, and handle normal variance and support-dependent uniform endpoints.
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Statistics
Discrete Bayesian Updating worksheets
Complete prior-likelihood-posterior tables, compare sequential and batch evidence, and handle zero priors or impossible evidence.
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Statistics
Bayesian Prediction and Odds worksheets
Form predictive mixtures, convert odds and probability, update odds with Bayes factors, and interpret evidence direction.
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Statistics
Continuous-Prior Bayesian Updating worksheets
Normalize polynomial prior-likelihood products, integrate evidence, predict future outcomes, and distinguish density from point mass.
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Statistics
Beta Conjugate Priors worksheets
Normalize integer-shape Beta densities, interpret strength, update Bernoulli/binomial/geometric data, and predict.
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Statistics
Normal Conjugate Priors worksheets
Update a normal mean with known observation variance using precision weights and verify sequential consistency.
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Statistics
Prior Choice and Sensitivity worksheets
Compare priors under identical data, contrast weak and strong priors, preserve zero prior mass, and justify prior choices.
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Statistics
Credible Intervals worksheets
Calculate discrete and continuous posterior interval mass, equal-tail intervals, interpretations, and quantile-based prior choices.
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Design and interpret a hypothesis test
Specify the hypotheses and rejection rule before calculating. Choose the correct data design and degrees of freedom; report uncertainty without treating a p-value as the probability of a hypothesis.
Statistics
Hypothesis Tests, Errors, and Power worksheets
Design null and alternative hypotheses, choose rejection sets, and compute Type I error, Type II error, and power.
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Statistics
Exact Binomial and Known-Sigma z Test worksheets
Run exact one- and two-sided binomial tests and known-sigma z tests from raw data or summaries.
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Statistics
One-Sample, Paired, Pooled, and Welch t Test worksheets
Select and run one-sample, paired, equal-variance pooled, and unequal-variance Welch t tests.
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Statistics
Chi-Square Goodness-of-Fit and Independence worksheets
Build expected counts and calculate Pearson X2 or likelihood-ratio G for categorical data.
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Statistics
One-Way ANOVA worksheets
Compute between and within sums of squares, complete ANOVA tables, and interpret omnibus F tests.
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Statistics
Bayesian Claims versus NHST Claims worksheets
Compare p-values, error rates, and posterior hypothesis probabilities without reversing their conditioning.
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Estimate with intervals and resampling
Match a z, t, chi-square, large-sample or bootstrap interval to its assumptions. State the quantile rule and interpret coverage correctly.
Statistics
Normal-Data Confidence Intervals worksheets
Construct z and t mean intervals, chi-square variance intervals, inspect coverage, and invert a two-sided test.
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Statistics
Large-Sample Confidence Intervals worksheets
Use conservative proportion bounds, the approximate 95% rule, and CLT intervals for general means.
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Statistics
Bootstrap Confidence Intervals worksheets
Build empirical PMFs, calculate supplied resample statistics, and form percentile and basic bootstrap intervals.
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Extend and assess a regression model
Evaluate squared error, inspect residual patterns and compare complexity using held-out information. Interpret a multiple-regression coefficient with the other predictor fixed.
Statistics
Least-Squares Curve Models worksheets
Compare supplied line, quadratic, cubic, and transformed exponential models using residuals and SSE.
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Statistics
Regression Model Diagnostics worksheets
Read finite residual plots, compare held-out errors, assess influential points, and reason about regression to the mean.
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Statistics
Multiple Regression Introduction worksheets
Use a supplied two-predictor equation to identify variables, predict, calculate residuals and SSE, and write the least-squares objective.
Preview and downloadKeep assumptions with the calculation
A small standard deviation describes concentration around a mean; it does not show that data are normally distributed. A correlation describes linear association; it does not establish cause and effect. Predictions outside the observed range need extra caution.
Choose a method whose assumptions fit the observations. Confidence intervals concern a repeated-sampling procedure; credible intervals describe posterior probability under a stated prior and likelihood.
Review data graphs · Review averages and range · Continue algebra and functions
Follow the college learning path
Connect random variables and sampling to Bayesian inference, tests, intervals and regression.
Introductory probability and statistics worksheets →