The Same Data, Six Charts

Axis limits, binning, aspect ratio, and colour scale — each one changes the story.

Ch 2 2.7

Comparator

Foundations & Data Quality

15 mindifficulty 2/5

Preparing…

Predict before you look

You truncate a scatter plot's y-axis so the trend line looks twice as steep on screen. What happens to the fitted regression slope reported underneath?

Scenarios

Teacher-ready starting points.

Documentation

What this shows

One generated dataset, rendered six different ways at once: a histogram whose bin count can hide or invent structure, a scatter plot whose y-axis limits and aspect ratio can exaggerate or flatten a slope, the same series on linear versus log scales, a group comparison shown as bars-of-means versus the full jittered distribution, the classic Anscombe's quartet where four datasets share every summary statistic but look nothing alike, and a heatmap whose colour scale can invent visual banding in a smooth field. The invariant readouts (n, mean, sd, r, slope) never change across any of these views.

Framing is a free parameter

A least-squares fit of y on x is completely determined by the data: slope = Σ(xᵢ−x̄)(yᵢ−ȳ) / Σ(xᵢ−x̄)². Nothing about the axis limits, the pixel aspect ratio, or the chosen colour palette enters that formula, yet all three change a viewer's perceived steepness, because visual angle — not the numeric slope — is what the eye estimates.

A histogram is a set of bin choices imposed on continuous data. With bin width h, a mode narrower than roughly 2h can be averaged away entirely, while random clustering inside overly narrow bins produces visible peaks with no population-level meaning — this is the bias/variance trade-off of density estimation made visible.

Anscombe's quartet fixes mean(x), mean(y), var(x), var(y), correlation r, and the OLS line across four datasets by construction, proving that the first five moments of a joint distribution can be identical while the shapes (linear, quadratic, single outlier driving the fit, near-vertical cluster) are completely different.

slope = Σ(xᵢ−x̄)(yᵢ−ȳ) / Σ(xᵢ−x̄)²

r = cov(x,y) / (sd(x)·sd(y))

perceived slope ∝ (Δy/Δx) · (pixel height / pixel width)  — Cleveland's banking-to-45°

Try this

Load the bimodal dataset with bins = 3, then push bins to 35 and watch the second mode appear, vanish, and fragment.
On the scatter panel, hold the linear dataset and cycle zero-based → truncated → padded y-limits. Read the slope number each time.
Drag the aspect ratio slider from wide to tall on the same regression line and describe how 'strong' the relationship looks at each extreme.
Switch the group comparison from bars to distribution and estimate, by eye, how much the groups overlap — then compare with the sd readouts.
Set the heatmap to rainbow and slide the midpoint: count how many false 'edges' appear in what is actually a smooth gradient.

Common misconception

“A chart is a neutral window onto the data — it just shows what's there.”

Every chart embeds choices that a viewer cannot see from the picture alone: bin width, axis limits, aspect ratio, linear-vs-log scale, level of aggregation, and colour mapping. None of those choices touch the underlying numbers, but all of them change the story a viewer walks away with. Reading a chart honestly means asking what was chosen before asking what it shows.

DSPA3 — Exploratory Visual Analytics