Unit 2 of 12

Describing and Exploring Data

  • 9 lessons
  • Videos 4 to 12

Tables, graphs and summary numbers describe what a set of data shows. This unit builds frequency tables and graphs, measures center, spread and position, and describes relationships.

Frequency tables and bar charts summarize categorical data, and dot plots and histograms show the shape of numerical data. With unequal bin widths, the heights of a histogram are frequency densities, so area shows the count. The mean, median and mode describe center, the variance and standard deviation describe spread, and percentiles, box plots and z-scores describe position. Scatter plots and correlation describe how two variables vary together, and two-way tables show how combining groups can reverse an association, which is Simpson's paradox.

Every lesson will be one video. The videos are coming soon, and each lesson page already has the definitions and an example for every key term.

Tables, Charts and Distribution Shape

  1. Frequency Tables and Categorical Charts

    How to build frequency tables with relative frequencies and a stated denominator, draw honest bar charts, and read contingency tables, conditional percentages, cumulative frequencies and multiple-response questions.

    Video 4

  2. Dot Plots, Histograms and Distribution Shape

    How dot plots and histograms show the distribution of numerical data, how bins and frequency density work when bin widths differ, and how to describe shape through symmetry, skewness, tails and modality.

    Video 5

Center, Spread and Position

  1. Mean, Median, Mode and Weighted Averages

    How the mean, median and mode measure the center of data, why the mean is a balance point, why the median resists extreme values, and how a weighted mean combines groups of different sizes.

    Video 6

  2. Variance and Standard Deviation

    How deviations from the mean build the population variance, the sample variance and the standard deviation, why a sample divides by one less than its size, and what degrees of freedom count.

    Video 7

  3. Percentiles, Quartiles and Box Plots

    How percentiles and quartiles locate positions in ordered data, how the interquartile range, five-number summary, box plot and outlier fences are built, and how the median absolute deviation and trimmed mean resist extreme values.

    Video 8

  4. Z-Scores and Changes of Scale

    What a z-score measures, how standardization rescales data to mean 0 and standard deviation 1, and how shifts, changes of scale, linear transformations and unit conversions affect the mean and spread.

    Video 9

Comparisons and Relationships

  1. Comparing Distributions and Reading Graphs

    How to compare whole distributions on a common scale, why bars need a meaningful baseline, how absolute change, relative change and percentage points differ, and how to recognize a misleading graph.

    Video 10

  2. Scatter Plots, Covariance and Correlation

    How a scatter plot shows paired data, how sample covariance and Pearson correlation measure linear association, how influential points and range restriction change them, and what Spearman rank correlation measures.

    Video 11

  3. Two-Way Tables and Simpson's Paradox

    How marginal and conditional percentages in a two-way table can disagree, why aggregation can reverse an association in Simpson's paradox, and how a standardized rate compares groups over a common mixture.

    Video 12