Chebyshev's Theorem Calculator

Calculate Range of Values (Chebyshev's Theorem)

Formula

The formula to calculate the range of values within a certain number of standard deviations from the mean, according to Chebyshev's Theorem, is:

\[ \text{Range} = \left(1 - \frac{1}{k^2}\right) \times 100\% \]

Where:

What is Chebyshev's Theorem?

Chebyshev's Theorem is a statistical rule that states for any given data sample, the proportion of observations is at least \( 1 - \frac{1}{k^2} \), for all \( k > 1 \), that fall within \( k \) standard deviations from the mean. This theorem provides a lower limit on the amount of data that falls within a certain number of standard deviations from the mean, allowing statisticians to make generalizations about data distribution. It applies to any distribution regardless of its shape.

Example Calculation

Let's assume the following value:

Using the formula to calculate the range of values:

\[ \text{Range} = \left(1 - \frac{1}{2^2}\right) \times 100\% = \left(1 - \frac{1}{4}\right) \times 100\% = 0.75 \times 100\% = 75\% \]

The range of values is 75%.