Five prompts covering the four things a distribution can tell you — shape, modality, spread, and extremes — plus the group-overlap question Week 6 turns on. Commit to an answer before revealing; the point is to find out which of these you can already read off the numbers without a chart.
Skew · predict before reveal
Course completion times have a mean of 14.2 weeks and a median of 11.5. Before anything is plotted — which tail is long, and which summary should the report lead with?
The mean sits above the median, so the long tail runs to the right: a minority of very slow completions drags the mean up while the median stays with the bulk of students. Lead with the median as the typical case, and use the mean only when the total is what matters — total tutor hours, total cost — saying which you chose. The \( 2.7 \)-week gap between them is itself the diagnostic, and it was readable before any chart existed.
Modality · predict before reveal
A histogram of exam scores shows a single peak at a bin width of 12 points and two peaks at a bin width of 4. Which reading belongs in the report?
Neither on its own. Bin width is a parameter you choose, so a mode that appears at one width and disappears at another is partly a claim about the smoothing. Show the distribution at more than one width and state whether the second mode survives. If it does, go looking for the subgroup that produces it — bimodality is usually two populations that were pooled, which is exactly what the bin-width explorer below is built from.
Spread · predict before reveal
Two campuses report the same mean score of 68. One has \( \mathrm{SD} = 4 \), the other \( \mathrm{SD} = 16 \). What changes for the reader?
Nearly everything. At \( \mathrm{SD} = 4 \) about two-thirds of students fall between 64 and 72; at \( \mathrm{SD} = 16 \) the same two-thirds span 52 to 84. The identical means license an identical headline and describe very different institutions — one where almost everyone sits near the middle, one where the middle is where hardly anybody is. A mean reported without a spread is half a sentence.
Outliers · predict before reveal
A single value of 240 appears in a set otherwise ranging from 30 to 95. Delete it, keep it, or something else?
Diagnose before deciding. Is it a data-entry slip (a 24.0 that lost its decimal point), a different unit, a genuine extreme, or a member of a different population altogether? Only the first two justify correcting the value, none justifies deleting it silently, and if it is genuine the defensible move is to report the analysis with and without it. “An outlier was removed”, with no diagnosis attached, is the sentence a reviewer stops on.
Group overlap · predict before reveal
Why can two groups with different means still overlap heavily in a visualization?
Because mean difference describes center, not the full distribution. Large within-group variation can create substantial overlap even when centers differ.
Distribution shape lab
The distribution shape lab needs JavaScript.
Effect-size lab
The effect-size lab needs JavaScript.
AI-output audit
This AI audit needs JavaScript.
Hands-on visual lab
These scores came from two distinct populations. Bin width is a parameter you choose, and it decides whether the reader can see that at all — including whether the second population survives the chart. Then run the browser-R lab below without leaving QuantegyAI.
This visual lab needs JavaScript.
R lab
R / Quarto / Shiny workflow
Build histogram/density/box plots and compare what each representation reveals or hides about group distributions.
# Suggested R workflow scaffold
library(tidyverse)
# 1. Import or construct the dataset
# 2. Verify summaries before visualizing
# 3. Build the ggplot2 visualization
# 4. Write the statistical interpretation and limitation note
# 5. Log any AI assistance and corrections
Module 3 Capstone
The inline Module 3 capstone submission and AI grader need JavaScript.
Adaptive reflection
What I know / where I go next
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Capstone connection Add this module’s evidence to your capstone readiness tracker. If your explanation depends on AI, include the prompt, output, verification method, and final correction.