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.

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## 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.

- First, determine the range (%).
- Next, determine the value of k (number of standard deviations from the mean).
- Next, use the formula: Range = (1 – 1/k^2) * 100% to calculate the percentage of values within k standard deviations of the mean.
- Finally, calculate the Chebyshev’s Theorem.
- 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