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# Chebyshev's Theorem Calculator

Formula Parameters:

$$P \ ( \ | \ X \ - \ E \ ( \ X \ ) \ | \ \geqslant \ k \ ) \ \leqslant \ \frac{σ^2}{k^2}$$

$$P \ ( \ | \ X \ - \ E \ ( \ X \ ) \ | \ \geqslant \ k \ ) \ \leqslant \ \frac{1}{k^2}$$

$$P \ ( \ | \ X \ - \ μ \ | \ < \ kσ \ ) \ \geqslant \ 1 \ - \ \frac{1}{k^2}$$

$$\sqrt{\frac{1}{1 \ - \ P \ ( x \ - \ μ \ < \ kσ )}}$$

Bound (k):

Variance (σ²):

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The free online Chebyshev’s Theorem Calculator calculates how much percentage of the data lies within the standard deviation of the mean of the set of data.

Chebyshev’s theorem calculator is a fast process to find all the probable values without finding the mean and standard deviation of data.

## Chebyshev’s Theorem Definition:

“The Chebyshev’s Theorem represents the %age of values within the “k” standard deviations”

What is the value of “k”?

The values of “k”= 1-(1/k^2)

It means for any shaped distribution, that at least  1-(1/k^2) data would be within the “k” deviation of the standard deviation of the mean.

• The values of “k”>1

### Chebyshev’s Theorem Formula:

The Chebyshev’s Theorem Formula is as follows:

$$P \ ( \ | \ X \ – \ μ \ | \ < \ kσ \ ) \ \geqslant \ 1 \ – \ \frac{1}{k^2}$$

Chebyshev’s theorem formula helps to find the data values which are 1.5 standard deviations away from the mean. When we compute the values from Chebyshev’s formula  1-(1/k^2), we get the 2.5 standard deviation from the mean value.  Chebyshev’s Theorem calculator allow you to enter the values of “k” greater than 1. The Chebyshev’s Inequality Calculator applies the Chebyshev’s theorem formula and provides you with a complete solution.

• Now substitute the value 5, we get the resultant values 1-(1/5^2), and when we compute the equation by chebyshev’s theorem calculator. We find the values equal to 96%. It means around 96 % of the data lies within the 5 standard deviations of the means. Here we don’t need to compute the standard deviation and the means value of the data. But if you still want to compute the standard deviation, you can do that by using another standard deviation calculator.
• If we are plugging the value of “3” for “k”, we insert the values in the formula  1-(1/3^2) and by computing the result by the chebyshev’s rule calculator. We get a result of 88.89% of data lying between the 3 standard deviations from the means. You can observe by adding the greater value of “k”, we are getting a more accurate estimation by the chebyshev calculator.

### Practical Example of Chebyshev’s Theorem Formula:

Substitute the value “k”=2,We find the value which is around 75 % of the data lies within the 2 standard deviations of the means.

k=2

P=?

Sol:

The probability formula:

$$P \ ( \ | \ X \ – \ μ \ | \ < \ kσ \ ) \ \geqslant \ 1 \ – \ \frac{1}{k^2}$$

Enter the value of “k”=2, we get

$$P \ ( \ | \ X \ – \ μ \ | \ < \ 2σ \ ) \ \geqslant \ 1 \ – \ \frac{1}{2^2}$$

$$P \ ( \ | \ X \ – \ μ \ | \ < \ 2σ \ ) \ \geqslant \ 1 \ – \ \frac{1}{4}$$

$$P \ ( \ | \ X \ – \ μ \ | \ < \ kσ \ ) \ \geqslant \ 1 \ – \ 0.250$$

$$P \ ( \ | \ X \ – \ μ \ | \ < \ kσ \ ) \ \geqslant \ 0.75$$

The probability calculated by chebyshev’s theorem calculator with mean and standard deviation is between 75%. It means 75% values would lie between our estimation by the chebyshev’s theorem formula.

### Working of Chebyshev’s Theorem Calculator:

Chebyshev’s calculator directly calculates  the probability without finding the mean values and the standard deviation of the data. Let’s find out how it actually works!

Input:

• Enter the values of  of “k”
• Hit the calculate button to find the probability

Output:

Chebyshev’s theorem calculator finds the probability of given data.

•  The final probability inequality is displayed
• Step by step procedure is done

### What does Chebyshev’s Theorem Formula describe?

Chebyshev’s Theorem or inequality tells us most of our data should fall in the % age given by chebyshev’s theorem calculator. We don’t need to find the lengthy calculation of finding the mean values and the standard deviation.

### How do you find Chebyshev in Excel?

We can use the Chebyshev in Excel by the following method:

• Type “=chebyshev(x)” into a blank cell

Where

“x” is the number of the Standard deviation .

The Excel will find Chebyshev’s theorem and return the Chebyshev’s theorem result.

### What is the “K” Chebyshev rule?

Chebyshev’s inequality describes that at least 1-1/K 2 of data must fall within the standard deviation of “K” from the mean values. Where k>1. Chebyshev’s inequality calculator finds all the possible values of the “k”.

### Conclusion:

Chebyshev’s Theorem calculator  provides us the probability values without finding the mean value and the standard deviation in a matter of seconds. It makes the whole estimation real simple and we can know the probable values of the data.Chebyshev’s theorem calculator provides us with the most efficient and swift result of Chebyshev’s theorem values.

### References:

From the source of Wikipedia: Chebyshev’s theorem, Chebyshev’s inequality

From the source of statisticsbyjim Chebyshev’s Theorem in Statistics, Equation for Chebyshev’s Theorem