De stelling van Tsjebysjev voor de interpretatie van de standaardafwijking

Chebyshev's theorem helps interpret the value of a standard deviation. It is applicable for almost all the datasets with normal, unknown, or skewed distributions.

In contrast, the empirical rule only applies to normally distributed data.

Consider the dataset of the lifespan of animals in a zoo, with a mean of 13 years and a standard deviation of 1.5 years.

According to Chebyshev's theorem, the proportion of animal ages within K standard deviations is at least one minus one divided by K squared. Here, K is any positive number greater than one.

For K equal to two, at least 75 percent of the animals' ages are within two standard deviations of the mean. Similarly, for K equal to three, at least 89 percent of the animal's ages fall within three standard deviations of the mean.

Although Chebyshev's theorem has wide statistical applications, it only provides lower limit approximations for standard deviations greater than one. It's important to note that Chebyshev's theorem provides only approximations.