STATLAB Academy | Learn Statistics with R and Real-World Data

Theory

Chebyshev's Theorem and the Empirical Rule

Compare a general lower bound with normal-shape benchmarks for intervals around the mean. The examples in this lesson use fictional STATLAB Academy business data and independently written explanations.

Explanation 1

Chebyshev works for any distribution when k is greater than 1.

Explanation 2

The Empirical Rule assumes an approximately normal shape.

Explanation 3

Observed proportions should be checked against assumptions.

Preparing your learning workspace

Chebyshev's Theorem and the Empirical Rule

Chebyshev's Theorem and the Empirical Rule

Chebyshev lower bound

Chebyshev's Theorem and the Empirical Rule

Empirical Rule Visualizer

R note: Chebyshev and the Empirical Rule

Chebyshev and the Empirical Rule

Results

Original applied scenario

Pause and write

Descriptive statistics coach

Lesson checkpoint

Chebyshev and Empirical Rule Checkpoint

Chebyshev's theorem guarantees at least what proportion within 2 standard deviations?