Chebyshev's Inequalities

Chebyshev's Inequality is a statistical concept that provides a way to estimate how much data varies around the average. It states that, regardless of the data's distribution shape, at least \(1 - \frac{1}{k^2}\) of the data falls within \(k\) times the standard deviation from the mean. For example, with \(k=2\), at least 75% of data is within two standard deviations of the average. This inequality helps us understand the spread and reliability of data even when the exact distribution is unknown.