Chebyshev's Inequality
Chebyshev's Inequality is a statistical theorem that provides a way to estimate the probability that a random variable deviates from its mean. Specifically, it states that for any real number k > 1 , at least 1 - \frac1k^2 of the values lie within k standard deviations from the mean. This means that even with limited information about the distribution, we can make reliable predictions about the spread of data.
This inequality is particularly useful because it applies to all types of distributions, not just the normal distribution. It helps in understanding the variability of data and is often used in fields like statistics, finance, and engineering to assess risk and make informed decisions.