Math101 · Independent Ontario learning library
11 · Subject library
Probability and Statistics
Data, uncertainty, distributions, inference, and sound statistical reasoning.
Start with Bar Graphs →40 complete · 40 total lessons
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01Bar GraphsA rigorous guide to bar graphs, categorical frequencies, scale choices, comparisons, and honest interpretation.Full lesson + sheet02Bayes' TheoremA precise treatment of Bayes' theorem, base rates, partitions, diagnostic tests, and interpretation.Full lesson + sheet03Bias in DataStatistical bias is a systematic tendency for a collection or analysis method to miss the truth in a particular direction.Full lesson + sheet04Bias in SamplingA rigorous guide to coverage, selection, nonresponse, response, and convenience bias in samples.Full lesson + sheet05Binomial DistributionThe binomial distribution models the number of successes in a fixed set of independent, equal-probability trials.Full lesson + sheet06Box PlotsA precise guide to five-number summaries, quartiles, IQR fences, skew, and responsible group comparison.Full lesson + sheet07Central Limit TheoremA rigorous account of central limit theorems, standardization, conditions, and limits of normal approximation.Full lesson + sheet08CombinationsCombinations count unordered selections, where only membership matters and rearranging the same chosen objects does not create a new outcome.Full lesson + sheet09Conditional ProbabilityConditional probability recalculates chance within the smaller sample space where given information is already known to be true.Full lesson + sheet10Confidence IntervalsA confidence interval combines a sample estimate with a margin of error to describe plausible values for a population parameter.Full lesson + sheet11CorrelationCorrelation measures the direction and strength of a linear relationship between two quantitative variables.Full lesson + sheet12Counting PrincipleA precise guide to the fundamental counting principle, decision trees, restrictions, and probability denominators.Full lesson + sheet13Data and VariablesA rigorous introduction to observational units, variables, datasets, coding, and the limits of measurement.Full lesson + sheet14Data CollectionGood data collection begins with a precise question, defined population and variables, ethical design, and a plan to reduce error.Full lesson + sheet15Discrete Probability DistributionsA rigorous guide to probability mass functions, cumulative probabilities, expectation, variance, and model checks.Full lesson + sheet16Expected ValueExpected value is the probability-weighted long-run average of a random variable.Full lesson + sheet17Frequency TablesA precise guide to frequency, relative and cumulative frequency tables, class intervals, and validation.Full lesson + sheet18Fundamental Counting PrincipleThe fundamental counting principle multiplies the number of choices across successive stages to count complete outcomes efficiently.Full lesson + sheet19HistogramsA rigorous guide to histogram bins, density, distribution shape, and defensible comparison.Full lesson + sheet20Hypothesis TestingA rigorous guide to null hypotheses, test statistics, p-values, errors, power, assumptions, and responsible conclusions.Full lesson + sheet21Independent EventsA precise treatment of independence, conditional probability, pairwise versus mutual independence, and common misconceptions.Full lesson + sheet22Linear RegressionLinear regression fits a least-squares line to paired quantitative data and uses residuals to assess predictions.Full lesson + sheet23MeanThe arithmetic mean is a balance-point average found by sharing a total equally across observations.Full lesson + sheet24MedianThe median is the ordered middle of a data set and provides a resistant measure of centre when values are skewed or contain outliers.Full lesson + sheet25ModeThe mode identifies the most frequent value or category and works with both numerical and categorical data.Full lesson + sheet26Normal DistributionThe normal distribution is a symmetric continuous model determined by its mean and standard deviation.Full lesson + sheet27One-Variable DataOne-variable data analysis describes the distribution of one measured characteristic through shape, centre, spread, and unusual values.Full lesson + sheet28PercentilesA rigorous guide to percentile ranks, quantiles, interpolation conventions, and responsible interpretation.Full lesson + sheet29PermutationsPermutations count ordered arrangements, where changing positions creates a different outcome.Full lesson + sheet30ProbabilityProbability quantifies uncertainty from impossible to certain and connects sample spaces, long-run frequency, counting, and decision making.Full lesson + sheet31Random VariablesA random variable assigns a numerical value to each outcome of a random process, creating a probability distribution.Full lesson + sheet32RangeRange is the distance from the minimum to maximum and gives a quick, outlier-sensitive measure of total spread.Full lesson + sheet33Sample SpacesA precise guide to outcomes, sample spaces, events, equally likely models, and structured enumeration.Full lesson + sheet34SamplingA rigorous guide to populations, frames, probability samples, stratification, clusters, and inferential scope.Full lesson + sheet35Sampling MethodsSampling methods determine how units enter a study and therefore how credibly sample results can represent a population.Full lesson + sheet36Scatter PlotsScatter plots display paired numerical data and reveal direction, form, strength, clusters, outliers, and possible associations.Full lesson + sheet37Standard DeviationStandard deviation is the square root of variance and describes typical distance from the mean in the data's original units.Full lesson + sheet38Types of DataA precise guide to categorical and quantitative data, measurement levels, discrete and continuous variables, and method choice.Full lesson + sheet39VarianceVariance measures average squared distance from the mean and forms the foundation of standard deviation.Full lesson + sheet40Z-ScoresA rigorous guide to standardization, sign and scale interpretation, normal probabilities, and comparison limits.Full lesson + 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