Statistics: all 163 lessons, free

Data and variables

9 lessons

Recorded facts about a group of individuals, where a variable is one thing recorded about each individual.

1.1Sorting objects into groupsKindergarten

1.2Counting each group and ordering groups by how manyKindergarten

1.3Data and variables

1.4Data tables, tallies and frequency tablesGrade 1

1.5Collecting data with a surveyMath 6

1.6Statistical questions and variabilityMath 6

1.7Types of data: categorical, numerical, discrete, continuousMath 6

1.8Individuals, variables and unitsMath 6

1.9Relative frequency tablesMath 8

Data displays

32 lessons

Pictures of data: which one to draw, and how to read it.

2.1Bar graphs and pictographs

2.2Data displays

2.3Picture graphs and their keyGrade 2

2.4Reading a bar graphGrade 2

2.5Making bar graphsGrade 2

2.6Line graphsGrade 5

2.7Making a dot plotGrade 2

2.8Reading dot plots: clusters, gaps and peaksGrade 2

2.9Line plots with fractionsGrade 5

2.10Reading a graph: titles, labels and unitsGrade 3

2.11Scaled picture graphsGrade 3

2.12Dot plots

2.13Choosing a display for a questionMath 6

2.14Stem and leaf plotsMath 6

2.15Circle graphsMath 6

2.16Histograms

2.17Making a histogram and choosing the bin widthMath 6

2.18Reading a histogramMath 6

2.19Misleading graphsMath 6

2.20Box plots

2.21Comparing box plotsMath 7

2.22Making and reading box plotsMath 6

2.23Plotting paired data: explanatory and response variablesMath 8

2.24Scatter plots

2.25Describing a scatter plotMath 8

2.26Association in a two way table and segmented bar graphsMath 8

2.27Conditional relative frequenciesMath 8

2.28Joint and marginal frequenciesMath 8

2.29Two-way tables

2.30Box plots that show outliersAlgebra 1

2.31Relative frequency histogramsAlgebra 1

2.32Cumulative frequency graphs and percentilesStatistics

Center and spread

27 lessons

One number for the middle, one number for how spread out.

3.1Mean as fair share: computing the meanGrade 5

3.2Mode and bimodal dataMath 6

3.3Finding the medianMath 6

3.4Center and spread

3.5Median and mode

3.6Quartiles and the five number summaryMath 6

3.7Range and interquartile range

3.8Mean

3.9Mean as balance pointMath 6

3.10Mean from a frequency table and weighted meanMath 6

3.11Mean absolute deviationMath 6

3.12Shape of a distribution

3.13Symmetric and skewed distributionsMath 6

3.14Uniform and bimodal shapesMath 6

3.15PercentilesAlgebra 1

3.16Outliers and the 1.5 IQR ruleMath 6

3.17Resistant and non resistant measuresMath 6

3.18Mean, median and skew: choosing the centerMath 6

3.19Describing a distributionMath 6

3.20Comparing two distributionsMath 7

3.21Comparing two populations: the gap between means in MADsMath 7

3.22Computing a standard deviation, sample and populationAlgebra 1

3.23Standard deviation

3.24Variance of a data setAlgebra 1

3.25Interpreting a standard deviationAlgebra 1

3.26Shifting and rescaling a data setAlgebra 1

3.27Standardizing a data setAlgebra 2

Sampling and study design

20 lessons

How data was collected decides what it can tell you.

4.1Populations, samples and censusMath 7

4.2Bias

4.3Random sampling

4.4Sampling and study design

4.5Convenience and voluntary response samplesMath 7

4.6Response bias and question wordingMath 7

4.7Control groups, placebos and blindingStatistics

4.8Observational studies and experimentsAlgebra 1

4.9Parameters and statisticsMath 7

4.10Simple random samples and the sampling frameMath 7

4.11Units, treatments, factors and levelsStatistics

4.12Random assignment and confoundingStatistics

4.13Cluster samples and choosing a designStatistics

4.14Comparing two treatments by re-randomizingAlgebra 2

4.15Stratified random sampleStatistics

4.16Systematic sampleStatistics

4.17Undercoverage and nonresponseStatistics

4.18Completely randomized design and replicationStatistics

4.19Blocking: randomized block and matched pairs designsStatistics

4.20Experimental design

Bivariate data

21 lessons

Two variables at once: is there a relationship, and how strong?

5.1Bivariate data

5.2Correlation

5.3Correlation is not causation: lurking and confounding variablesAlgebra 1

5.4Line of best fitMath 8

5.5Interpreting a residualAlgebra 1

5.6Interpreting the slope and interceptMath 8

5.7Predicting with a regression line, and extrapolationAlgebra 1

5.8Properties of the correlation coefficientAlgebra 1

5.9The correlation coefficientAlgebra 1

5.10Fitting linear and exponential models with technologyAlgebra 1

5.11Correlation from standardized valuesStatistics

5.12Making and reading residual plotsAlgebra 1

5.13Outliers, leverage and influential pointsStatistics

5.14r squared and the standard deviation of the residualsStatistics

5.15Slope from r and the spreads, and regression to the meanStatistics

5.16The least squares criterion and its lineStatistics

5.17Least squares regression

5.18Reading regression outputStatistics

5.19Residuals

5.20Transforming to linearity: logs and exponential modelsStatistics

5.21Log-log transforms and power modelsStatistics

Distributions

16 lessons

Models for how values are spread, and the normal curve above all.

6.1Sampling variability and simulating itMath 7

6.2Density curves: area, mean and medianAlgebra 2

6.3Simulating a sampling distribution and a margin of errorAlgebra 2

6.4The standard normal distributionAlgebra 2

6.5Normal calculations: areas and percentilesAlgebra 2

6.6Distributions

6.7The central limit theoremStatistics

6.8The normal distributionAlgebra 2

6.9Bias and variability of an estimatorStatistics

6.10Checking whether data look normalAlgebra 2

6.11Sampling distributions

6.12The ten percent conditionStatistics

6.13z-scores and the empirical ruleAlgebra 2

6.14Sampling distribution of a sample meanStatistics

6.15Sampling distribution of a sample proportionStatistics

6.16Sampling distribution of a differenceStatistics

Statistical inference

38 lessons

From a sample to a claim about the population, with honest uncertainty.

7.1Confidence intervals

7.2Confidence level and interpreting an intervalStatistics

7.3Hypothesis testing

7.4Null and alternative hypothesesStatistics

7.5Point estimates and the margin of errorStatistics

7.6Standard errorStatistics

7.7Statistical inference

7.8Test statisticStatistics

7.9Chi-square tests

7.10p-values and the significance levelStatistics

7.11Deciding and concluding from a p-valueStatistics

7.12Type I and Type II errorsStatistics

7.13Cautions about significanceStatistics

7.14Power and what raises itStatistics

7.15Inference for slopes

7.16Sampling distribution of the slopeStatistics

7.17Conditions for one meanStatistics

7.18Conditions for regression inferenceStatistics

7.19Inference for means

7.20The t distribution and degrees of freedomStatistics

7.21Critical valueStatistics

7.22Expected counts and the chi-square statisticStatistics

7.23One sample test for a meanStatistics

7.24Conditions for one proportionStatistics

7.25Goodness of fit testStatistics

7.26Inference for proportions

7.27One sample interval for a mean and sample sizeStatistics

7.28Interval for a difference of meansStatistics

7.29Interval for a slopeStatistics

7.30One sample interval for a proportion and sample sizeStatistics

7.31One sample test for a proportionStatistics

7.32Tests for independence and homogeneityStatistics

7.33Choosing the right procedureStatistics

7.34Interval for a difference of proportionsStatistics

7.35Test for a difference of meansStatistics

7.36Test for a slopeStatistics

7.37Paired data: interval and test for a mean differenceStatistics

7.38Test for a difference of proportionsStatistics