Enter the range and number of standard deviations into the calculator to determine the percentage of values within a certain number of standard deviations from the mean according to Chebyshev’s Theorem.

Chebyshevs Theorem Formula

The following formula is used to calculate the range of values within a certain number of standard deviations from the mean, according to Chebyshev’s Theorem. 

Range = (1 - 1/k^2) * 100%

Variables:

  • Range is the percentage of values within k standard deviations of the mean
  • k is the number of standard deviations from the mean

To calculate the range of values within a certain number of standard deviations from the mean, subtract 1 divided by the square of the number of standard deviations from 1. Multiply the result by 100 to convert it to a percentage.

What is a Chebyshevs Theorem?

Chebyshev’s Theorem is a statistical rule that states for any given data sample, the proportion of observations is at least (1-(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.

How to Calculate Chebyshevs Theorem?

The following steps outline how to calculate the Chebyshev’s Theorem.

  1. First, determine the range (%). 
  2. Next, determine the value of k (number of standard deviations from the mean). 
  3. Next, use the formula: Range = (1 – 1/k^2) * 100% to calculate the percentage of values within k standard deviations of the mean.
  4. Finally, calculate the Chebyshev’s Theorem.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Range (%) = 80

k = 2