Domain: Natural Science — Statistics & Data Science
Target concept: Variance

Video generation prompt: Box plots of the two datasets are displayed side by side, with the left dataset exhibiting smaller variance and the right dataset exhibiting larger variance. The comparison of the box plots on both sides is used to illustrate the difference in variance.

Evaluation guide:
Target concept: Variance as a quantitative measure of statistical dispersion, operationally defined by squared deviations from the mean, but visualized intuitively via box plot geometry. Minimum mechanistic assumption: Box plots encode dispersion through IQR width and whisker length, and human visual system reliably discriminates relative spread when plots are aligned, scaled identically, and labeled unambiguously. Phased storyline: (1) Static reveal of two side-by-side box plots with explicit low-/high-variance labels; (2) 3-second dwell highlighting left plot’s narrow box/short whiskers → perceptual cue for concentration; (3) 3-second dwell highlighting right plot’s wide box/long whiskers → perceptual cue for dispersion; (4) 2-second simultaneous comparison with overlaid annotation: ‘Same scale, different spread → different variance’. Visibility constraints: Frontal, orthographic view; no occlusion; text labels must be legible at 1080p; color contrast ≥4.5:1 (WCAG AA); all elements must remain stable for ≥2 seconds to enable visual scanning and comparison.

Manual:
I. Basic Demonstration Information
Demonstration Title: Variance Comparison via Side-by-Side Box Plots Demonstration
Subject: Natural Science - Statistics & Data Science - Variance
Demonstration Purpose: To visually illustrate variance as a measure of data spread by displaying two box plots side-by-side — left showing a low-variance dataset (narrow IQR, short whiskers), right showing a high-variance dataset (wide IQR, long whiskers); enables direct visual recognition of how box plot geometry encodes variability.
II. Demonstration Carrier/Equipment
Core Carrier: Two synthetic numeric datasets (left: N=30, σ²≈4; right: N=30, σ²≈36), pre-computed to yield clearly distinguishable box plot geometries.
Auxiliary Equipment: Static visualization canvas (1920×1080, white background), standardized box plot renderer (matplotlib/seaborn style), clear sans-serif font (size ≥24), color-coded labels (blue for left, red for right), shared y-axis with numeric ticks.
III. Demonstration Content Description
Layout: Left plot occupies 45% width, right plot 45%, 10% gap center-aligned; both share identical y-axis range (e.g., 0–100) and tick marks.
State Control: Both plots rendered statically (no animation within plots); labels appear simultaneously with plots and persist.
Comparison Baseline: Identical sample size (N=30), same measurement unit, same axis scaling — isolating variance as sole differing factor.
IV. Observation of Core Phenomena
Left Plot Characteristics: Compact rectangular box (small IQR), short vertical whiskers extending minimally above/below box, tightly clustered outliers (≤2 points), median line centered — conveys data concentration.
Right Plot Characteristics: Elongated rectangular box (large IQR), long vertical whiskers extending far beyond box, scattered outliers (≥5 points), median line still centered — conveys data dispersion.
Characteristic Stability: Geometry remains invariant across observation window; no flicker, drift, or rescaling; variance contrast is immediate and resolution-independent.
Auxiliary Comparison: Shared axis and labeling eliminate scale confusion; color coding (blue/red) reinforces left/right semantic distinction without ambiguity.
V. Summary of Key Knowledge Points and Principles
Core Concept Definition: Variance quantifies how far a set of numbers is spread out from their average value; higher variance = greater dispersion.
Visual Encoding Principle: In box plots, Interquartile Range (IQR = Q3−Q1) is the primary visual proxy for variance; whisker length and outlier count provide secondary cues. Narrow IQR + short whiskers → low variance; wide IQR + long whiskers → high variance.
Why Box Plots?: They summarize distribution shape, central tendency, and spread in one compact graphic — ideal for comparative variance illustration without requiring raw data literacy.
VI. Demonstration Precautions
Scaling Integrity: Never use different y-axis ranges or truncated axes — this would distort perceived variance.
Label Clarity: Labels must be unambiguous (e.g., ‘Low-Variance Dataset’ above left, ‘High-Variance Dataset’ above right); avoid generic ‘Group 1/2’.
Rendering Fidelity: Use deterministic random seeds for dataset generation to ensure reproducible spread; avoid jitter or smoothing that masks true dispersion.

Prompt Grounding rubric:
level_1: No box plots appear anywhere in the frame, or only one plot is shown instead of two; the two datasets are stacked one above the other or shown in separate scenes rather than side by side; neither plot carries a label identifying it as the low- or high-variance dataset; or the left and right boxes and whiskers look identical in size, so there is no visible difference in spread to compare.
level_2: Two box-plot shapes sit side by side, but it is unclear which is meant to be lower- and which higher-variance: labels are missing, contradictory, or placed on the wrong plot, and the left and right boxes/whiskers are drawn at nearly the same width and length; some other chart element (an axis line, a title) may be present, but the core narrow-left/wide-right contrast the prompt calls for is missing.
level_3: The two box plots sit correctly on the left and right with legible labels distinguishing the datasets (e.g., 'Dataset A'/'Dataset B' or 'Low Variance'/'High Variance'); the left box and whiskers are visibly narrower and shorter than the right box and whiskers; clarity is nonetheless reduced by a rendering flaw, such as a missing median line in one or both boxes, no outlier markers even where the whiskers imply some should exist, or the two plots sitting on differently scaled vertical axes so a direct comparison is harder to make.
level_4: The left and right box plots are correctly labeled, share one common vertical scale, and each shows a centered median line, a box, and whiskers; the left box/whiskers are clearly more compact than the right box/whiskers, giving an unambiguous low-versus-high spread contrast; only cosmetic shortcomings remain: a faint gridline, a plain monochrome color scheme, or a slightly truncated axis label, none of which get in the way of the comparison.
level_5: Both box plots are labeled explicitly (e.g., 'Low-Variance Dataset' on the left, 'High-Variance Dataset' on the right), share one continuous vertical axis and matching plot size, and each shows a centered median line, a box, whiskers, and any outlier points as small marks beyond the whiskers; the left box reads as visibly compact and the right box as visibly wide, so a viewer glancing at the frame for a moment can immediately tell which dataset is more spread out, with no mislabeling, scale mismatch, or rendering glitch anywhere in the frame.

Scientific and Causal Correctness rubric:
level_1: Box plots display physically impossible features (e.g., median outside IQR, negative whiskers, inverted order); or variance relationship contradicts statistical logic (e.g., right plot narrower than left despite being labeled 'high variance'); or plots represent histograms/dot plots instead of box plots; causal link between plot geometry and variance concept is absent or inverted.
level_2: The wider box does sit on the correct (high-variance) side, but the size difference looks arbitrary rather than grounded in the data: the box or whiskers appear stretched without the median or quartile edges moving in a way consistent with real data, so the picture reads as 'a shape made bigger' rather than 'a distribution with genuinely more spread'; nothing in the frame ties the width difference back to an actual variance value or ratio; or the whiskers on one or both boxes extend well beyond the standard ~1.5×IQR reach with no outlier points marked past them, breaking the usual box-plot convention for where a whisker should stop.
level_3: The high-variance plot's larger box and whiskers and the low-variance plot's smaller box and whiskers are each internally consistent (median inside its own box, whiskers extending outward rather than crossing the box, and each plot's whiskers roughly following the standard ~1.5×IQR convention with only points beyond that marked separately as outliers), and the size difference plausibly reflects a real difference in dispersion; however nothing on screen quantifies or names the variance values behind the two datasets, so the link between the picture and the variance concept is only implied, not reinforced.
level_4: The spread relationship is scientifically coherent throughout: the high-variance box's interquartile range and whisker reach are clearly and substantially larger than the low-variance box's, with whiskers on both boxes terminating at the standard ~1.5×IQR fence and any points beyond that fence rendered as distinct outlier markers rather than absorbed into the whisker line; both medians sit at plausible, non-extreme positions within their own boxes; and an on-screen label or caption explicitly ties the visual spread difference to the variance concept (e.g., stating that the right-hand dataset has greater variance than the left); nothing in the pair is statistically implausible.
level_5: Every visual cue reinforces the science of variance without contradiction: the low-variance box's tight interquartile range and short whiskers read as data clustered near its mean, the high-variance box's wide interquartile range and long whiskers read as data spread far from its mean, any outlier points shown are more numerous or more scattered on the high-variance side (consistent with greater dispersion producing more extreme values), both medians sit at reasonable positions, and an accompanying label correctly states that a wider box and longer whiskers indicate greater variance; the image is a faithful, unforced illustration of the concept.

Spatiotemporal Consistency rubric:
level_1: The two box plots never appear together in one stable view: for example, the left plot fades in and the right plot only appears afterward in a separate moment, or the plots visibly shift position, change size, or swap sides partway through; labels appear only after a plot has already vanished, so at no point can the full side-by-side comparison actually be seen.
level_2: Both plots do stay on screen at once, but the pairing does not read as coherent: the two boxes are drawn at noticeably different heights or widths unrelated to their underlying data, the vertical axes look inconsistent with each other (different range, or no numbers at all on one), or a label drifts away from the plot it is meant to describe; the plots also snap into view abruptly from a blank screen with no sense of easing in.
level_3: The left and right plots hold a stable side-by-side arrangement with what looks like a shared vertical scale, and each label stays attached to its own plot in a consistent spot (e.g., the dataset name centered above its box); a minor blemish remains (one plot settling into place a beat after the other, a brief flicker during the hold phase, or a slight drift in where an axis tick sits), but it does not undermine the overall left/right comparison.
level_4: Both plots share a matching axis range, comparable label size, and consistent spacing from the frame edge; each label (e.g., 'Low Variance' over the left plot, 'High Variance' over the right) stays legible and correctly positioned for the several seconds the comparison is meant to hold; the two plots fade in together, hold steady through a clear multi-second comparison window, and fade out cleanly, with no visible warping, tilting, or perspective shift of either plot.
level_5: The pairing reads as fully synchronized and stable throughout: both plots appear at the same moment with matching size, margins, and spacing so the layout looks mirrored left to right; both vertical axes carry the same scale, gridlines, and label style; the labels keep a consistent font, weight, and color scheme across the whole hold phase; the camera view stays frontal and static with no zoom or pan for the entire clip; and the two plots keep the same relative position and size in every frame of the hold phase, so a viewer could pause the video at any point during the comparison and still see the identical narrow-left/wide-right layout.