Representations of data
Turn data into useful pictures and explain what those pictures can—and cannot—show.
Work through thirteen lessons on outliers, box plots, cumulative frequency, histograms and contextual comparisons. Finish with independent mixed practice.
- Outliers and IQR fencesCalculate IQR fences, handle values exactly on a threshold and explain why an outlier flag calls for investigation. Original model, animation and worked practice.
- Outliers using mean and standard deviationUse mean plus or minus a multiple of standard deviation to investigate unusual values, while keeping the rule, denominator, precision and assumptions explicit.
- Investigating and cleaning dataDistinguish unusual observations from errors and out-of-scope records, document justified changes and recompute summaries correctly. Original scenarios and worked practice.
- Drawing box plotsBuild box plots from ordered data, distinguish outlier fences from observed whiskers, label scales and avoid inventing endpoints from incomplete summaries.
- Comparing box plotsCompare medians and interquartile ranges on shared scales, distinguish IQR from full range and avoid unsupported claims about individuals, means or causes.
- Cumulative frequency diagramsBuild running totals, plot at true upper class boundaries and distinguish known cumulative points from assumptions used between them. Original graph model and worked practice.
- Reading cumulative frequency diagramsEstimate medians and percentiles, read counts below and between thresholds and compare unequal sample sizes using cumulative percentages.
- Histograms and frequency densityUnderstand why histogram area represents frequency, calculate frequency density for unequal classes and distinguish bar height from count. Original adjustable model and worked questions.
- Histogram areas and estimated countsRecover complete class counts and estimate threshold or interval counts using histogram areas, with explicit uniformity assumptions and appropriate precision.
- Scaled histograms and missing informationCalibrate histogram areas from a known frequency, distinguish physical drawing units from data units and solve missing heights, widths and counts.
- Frequency polygonsPlot class-midpoint polygons, label frequency or density axes correctly and explain the effect of unequal class widths and endpoint conventions.
- Comparing distributions in contextCompare location and spread with units and context, choose robust summaries, account for sample sizes and avoid unsupported claims about individuals, thresholds or causation.
- Data representations: mixed practiceIndependent mixed questions on outliers, box plots, cumulative frequency, histograms, scale calibration and contextual comparisons, with worked solutions and assumption checks.