Statistics Fundamentals

Statistics is the grammar of science. Whether you're analysing experimental data, building machine-learning models, or simply reading a poll, you need a handful of core ideas to make sense of numbers. This post covers the essentials interactively — drag the sliders, watch the plots change, and build real intuition.

1. Central Tendency

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Distribution

Sample Size500

Add Outlier (200)

Mean: 49.87

Median: 49.32

Mode: 48.03

Std Dev: 10.09

2. Standard Deviation

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Mean (\u03BC)0

Sigma 1 (\u03C3\u2081)1

Sigma 2 (\u03C3\u2082)2

3. Empirical Rule (68-95-99.7)

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Mean (\u03BC)0

Std Dev (\u03C3)1

Sigma Range

1\u03C32\u03C33\u03C3

4. Z-Scores

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Value (x)

Mean (\u03BC)

Std Dev (\u03C3)

z = (x \u2212 \u03BC) / \u03C3 = 1.400

Moderate (|z| ≥ 1)

5. Confidence Intervals

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Sample Mean (\u0078\u0304)

Population \u03C3

Sample Size (n)30

Confidence Level

Std Error: 2.739

Margin of Error: \u00B15.368

CI: [94.63, 105.37]

6. Playground

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True Mean (\u03BC)0

True Std Dev (\u03C3)10

Sample Size500

Sample Mean: -0.13

Sample Std: 10.09

Sample Median: -0.68

True \u03BC: 0.0

True \u03C3: 10.0

Quick Reference

Concept	Symbol	What it tells you
Mean	$\bar{x}$	Average value
Median	—	Middle value (robust to outliers)
Mode	—	Most common value
Variance	$\sigma^2$	Average squared spread
Std Deviation	$\sigma$	Spread in original units
Z-score	$z$	How many σ from the mean
Confidence Interval	CI	Range likely containing the true parameter

Statistics Fundamentals

1. Central Tendency

2. Standard Deviation

3. Empirical Rule (68-95-99.7)

4. Z-Scores

5. Confidence Intervals

6. Playground

Quick Reference

Further Reading