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:
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.
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%.