“The Chebyshev's Theorem represents the %age of values inside the “k” fashionable deviations”
what is the value of “k”?
The values of “k”= 1-(1/ok^2)
It approach for any fashioned distribution, that as a minimum 1-(1/ok^2) statistics would be within the “k” deviation of the standard deviation of the suggest.
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.
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.
Chebyshev's Theorem or inequality tells us maximum of our statistics have to fall in the % age given by means of chebyshev's theorem calculator. We don’t need to locate the prolonged calculation of finding the imply values and the standard deviation.
Chebyshev's inequality describes that as a minimum 1-1/ok 2 of information have to fall in the standard deviation of “ok” from the mean values. wherein okay>1. Chebyshev's inequality calculator unearths all the feasible values of the “okay”..
