Read the world in data,
one belt at a time.

Before you can reason about data you have to see it. Learn to read a histogram, find the center of a batch of numbers with the average and the median, and measure its spread with the standard deviation — the three numbers that summarize almost any dataset.

1. 🔢
   Level 1 Variables & Distributions ★★★ ◆
2. 🔒
   Level 2 Histograms & the Density Scale ★★★ ◆ Needs: L01
3. 🔒
   Level 3 The Average & the Median ★★★ ◆ Needs: L02
4. 🔒
   Level 4 The Standard Deviation ★★★ ◆◆ Needs: L03
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   Level 5 · EXAM Describing Data Exam ★★★ ◆◆ Needs: L04

Chance is a number between 0 and 1, and it obeys just two rules — add for 'or', multiply for 'and'. Build probability from the ground up, learn where independence breaks down, and meet the box model: the single picture Freedman uses to reason about every game of chance.

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   Level 6 What Is Chance? ★★★ ◆ Needs: L05
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   Level 7 Adding & Multiplying Chances ★★★ ◆◆ Needs: L06
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   Level 8 Conditional Probability ★★★ ◆◆ Needs: L07
4. 🔒
   Level 9 The Box Model: Expected Value & SE ★★★ ◆◆◆ Needs: L08
5. 🔒 👑
   Level 10 · EXAM Chance Exam ★★★ ◆◆◆ Needs: L09

The same bell-shaped curve turns up everywhere — test scores, heights, measurement errors, chance sums. Learn to convert any value to standard units, read areas off the normal curve, and use the 68-95-99.7 rule to answer 'how unusual is this?' at a glance.

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   Level 11 Standard Units ★★★ ◆◆ Needs: L10
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   Level 12 The Normal Curve & the 68-95-99.7 Rule ★★★ ◆◆ Needs: L11
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   Level 13 Percentiles & the Normal Table ★★★ ◆◆◆ Needs: L12
4. 🔒
   Level 14 The Normal Approximation for Chances ★★★ ◆◆◆ Needs: L13
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   Level 15 · EXAM Normal Curve Exam ★★★ ◆◆◆ Needs: L14

When two things vary together, how do you measure it — and how do you predict one from the other? Read scatter diagrams, put a number on association with the correlation coefficient, fit the regression line, and learn the traps: outliers, the regression effect, and why correlation is not causation.

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   Level 16 Scatter Diagrams & Association ★★★ ◆◆ Needs: L15
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   Level 17 The Correlation Coefficient ★★★ ◆◆◆ Needs: L16
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   Level 18 The Regression Line ★★★ ◆◆◆ Needs: L17
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   Level 19 Prediction & RMS Error ★★★ ◆◆◆ Needs: L18
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   Level 20 · EXAM Correlation & Regression Exam ★★★ ◆◆◆ Needs: L19

This is the whole point. A sample is small and random, the truth is large and fixed — how do you cross the gap? Meet the central limit theorem and the standard error, build confidence intervals, run tests of significance, and finish with the chi-square test. Earn your black belt.

1. 🔒
   Level 21 Samples, Populations & Bias ★★★ ◆◆ Needs: L20
2. 🔒
   Level 22 The Central Limit Theorem & Standard Error ★★★ ◆◆◆ Needs: L21
3. 🔒
   Level 23 Confidence Intervals ★★★ ◆◆◆ Needs: L22
4. 🔒
   Level 24 Tests of Significance ★★★ ◆◆◆◆ Needs: L23
5. 🔒
   Level 25 The Chi-Square Test ★★★ ◆◆◆◆ Needs: L24
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   Level 26 · EXAM The Black Belt Exam ★★★ ◆◆◆◆ Needs: L25