Question

Given a group of data with mean 40 and standard deviation 5, at least what percent of data will fall between 15 and 45? Use Chebyshev's theorem. If you use 15 as the lower range limit, then you get k=5, and then the percent of data between 15 - 40 is (1-1/5^2)/2. If you use 45 as the upper range limit, then k=1. How to find the percent of data between 40 - 45?

Answer 1

We know that the chebyshev inequality theorem is applicable only when the two values coincide, i.e. when two values are at equal distance from the mean, then only we get the k for the chebyshev distribution.

In this case, 15 is 5 standard deviations below the mean. So, we get k = 5

and 45 is 1 standard deviation above the mean. So, we get k =1

Here we can see that the k value for 15 and 45 are not equal. This means that it is not appropriate to use chevyshev inequality rule in this case.

we must have k >1 in order to apply the chebyshev theorem.

So, we cannot apply chebyshev's theorem in this case.