Which of the following inequality is useful for interpreting variances?

Chebyshev
Stautaory
Testory
All of the mentioned

The correct answer is: A. Chebyshev

Chebyshev’s inequality is a mathematical inequality that provides a bound for the probability that a random variable will deviate from its mean by a certain amount. The inequality states that for any random variable $X$ with mean $\mu$ and variance $\sigma^2$, the probability that $|X-\mu|\ge k\sigma$ is less than or equal to $\frac{1}{k^2}$.

Chebyshev’s inequality is useful for interpreting variances because it provides a way to quantify the amount of variability in a data set. For example, if we know that the variance of a data set is 10, then Chebyshev’s inequality tells us that the probability that any data point is more than 20 units away from the mean is less than or equal to $\frac{1}{4}$. This information can be helpful in understanding the spread of the data and in making inferences about the population from which the data was sampled.

The other options are incorrect because they are not inequalities that are useful for interpreting variances. Stautaory and Testory are not real words.