The Chebyshev 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 distribution, at least 1 - \frac1k^2 of the values will fall within k standard deviations from the mean, where k is any positive number greater than 1. This means that even with limited information about the distribution, we can make useful predictions about the spread of data. This inequality is particularly valuable 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 finance and engineering to assess risk and reliability. By using the Chebyshev inequality, analysts can make informed decisions based on the likelihood of extreme values occurring.