Topics
Activities
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Types of Data
Classify variables step by step: qualitative or quantitative, nominal or ordinal, discrete or continuous.
- Collecting data
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Sampling Methods
Draw five kinds of samples from 1,000 employees and compare each statistic with the parameter.
- Collecting data
- Sampling variability
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Frequency Distributions, Bar Graphs, and Pie Charts
Turn qualitative data into a frequency distribution, a bar graph, a Pareto chart or a pie chart.
- Graphing data
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Histogram Builder
Change the class width and the lower limit of the first class, and watch the histogram change.
- Graphing data
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Visualizing Small Data Sets
See a small data set as a stem-and-leaf plot and a dotplot, side by side.
- Graphing data
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Mean vs. Median with Outliers
Drag one value far from the rest: the mean follows it, and the median barely moves.
- Mean and median
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Skewness Explorer
Skew a distribution to the left or the right and watch where the mean and the median fall.
- Mean and median
- Graphing data
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Building Variance and Standard Deviation
Watch each deviation and squared deviation build the variance and the standard deviation.
- Standard deviation
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Comparing Values with z-Scores
Put values from different distributions on one scale: standard deviations from their own mean.
- z-scores
- Standard deviation
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Correlation Explorer
Add or drag points on a scatterplot and watch the correlation coefficient r change.
- Correlation and regression
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The Least-Squares Regression Line
Move a line through a scatterplot and find the one that makes the total area of the squares smallest.
- Correlation and regression
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Law of Large Numbers
Repeat an experiment again and again and watch the proportion approach the probability.
- Probability
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Venn Diagram Probability Explorer
Set the probabilities and see a Venn diagram drawn to scale, with each rule worked out.
- Probability
- Conditional probability
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The Binomial Distribution
Choose n and p, and see which bars of the probability histogram add up to the probability.
- Binomial distribution
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Benford’s Law: Detecting Fraud
Compare the first digits of three expense reports with Benford’s law and find the made-up one.
- Probability
- Binomial distribution
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From Histogram to Density Curve
Make the classes narrower and watch a histogram’s outline become a probability density curve.
- Normal distribution
- Graphing data
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Normal Curve Explorer
Change μ and σ and see how each one shapes the normal curve.
- Normal distribution
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Normal Probability Calculator
Shade an area under a normal curve and find it with technology.
- Normal distribution
- z-scores
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Normal Percentile Calculator
Start with an area, find its z-score, and convert back to a value of x.
- Normal distribution
- z-scores
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Central Limit Theorem Machine
Draw samples and watch the sampling distribution of x̄ become approximately normal.
- Sampling variability
- Normal distribution
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Central Limit Theorem Machine for Proportions
See when the sampling distribution of p̂ is approximately normal: np and n(1 − p) at least 10.
- Sampling variability
- Normal distribution
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Assessing Normality
Compare pairs of samples on a dotplot and a boxplot: outliers, skewness and modes.
- Normal distribution
- Graphing data
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Student’s t Distribution
Compare the t curve with the standard normal curve as the degrees of freedom change.
- Confidence intervals
- Normal distribution
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Confidence Intervals for a Mean
Generate many confidence intervals and see how often they cover μ.
- Confidence intervals
- Sampling variability
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Confidence Intervals for a Proportion
Generate many confidence intervals and see how often they cover p, by two methods.
- Confidence intervals
- Sampling variability
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What Is a P-Value?
Assume H0 is true, simulate thousands of samples, and see what the P-value counts.
- Hypothesis testing
- Sampling variability
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One Sample, Three Null Hypotheses
Test one sample against three values of μ: not rejecting H0 does not mean H0 is true.
- Hypothesis testing
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Type I and Type II Errors
Run many tests and see how often each error happens, and what changes the power.
- Hypothesis testing
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The Multiple Testing Problem
Test 20 restaurant locations when every H0 is true, then adjust with Bonferroni.
- Hypothesis testing