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For Students · Clustering Workbench

Clustering Workbench for a dice-fairness check

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a dice-fairness check live below — adjust the inputs and watch it respond, right in your browser.

k-Means ClusteringLive

Controls

Presets

Lloyd's algorithm: assign each point to its nearest centroid, then move each centroid to the mean of its members. Repeat until stable. Try setting k different from the true cluster count.

▶ Run in Python

Data Inspector

Iteration0
Inertia0.00e+0
k4

Governing equation

Reading this result: k matches the 4 true clusters, so each centroid can settle onto one real group and inertia falls to a clean minimum.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Principal Component AnalysisLive

Controls

Presets

PCA finds the directions along which data varies most. The eigenvectors of the covariance matrix are the principal components (cyan = most variance, green = least), and their eigenvalues are the variances along each. Projecting onto the top components is the basis of dimensionality reduction.

▶ Run in Python

Data Inspector

Variance PC10.00
Variance PC20.00
PC1 explains0%
PC1 angle0°

Governing equation

Reading this result: PC1 explains 0% of the variance here; the stronger the correlation between features, the more PCA concentrates information on that first component.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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More with Clustering Workbench

Frequently asked questions

Is this good for students?
Yes — this version of "Clustering Workbench for a dice-fairness check" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?
No. It runs in any modern browser, free, with no account required.