SOLUTION: According to Chebyshev's theorem, the proportion of values from a data set that is further than 2 standard deviations from the mean is at most-----?

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Question 206150: According to Chebyshev's theorem, the proportion of values from a data set that is further than 2 standard deviations from the mean is at most-----?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
According to Chebyshev's theorem, the proportion of values from a data set that is further than 2 standard deviations from the mean is at most-----?

All you have to do is learn Chebyshev's theorem in terms of k, then 
substitute 2 for k.

Here is Chebyshev's theorem in terms of k:

According to Chebyshev's theorem, the proportion of values 
from a data set that is further than k standard deviations 
from the mean is at most 1%2Fk%5E2.

Then when you plug in 2 for k, you get:

According to Chebyshev's theorem, the proportion of values 
from a data set that is further than 2 standard deviations 
from the mean is at most 1%2F2%5E2.

or writing 4 for 2%5E2,

According to Chebyshev's theorem, the proportion of values 
from a data set that is further than 2 standard deviations 
from the mean is at most 1%2F4.

Or if you prefer a decimal answer:

According to Chebyshev's theorem, the proportion of values 
from a data set that is further than 2 standard deviations 
from the mean is at most 0.25.

Or if you prefer a percent answer:

According to Chebyshev's theorem, the proportion of values 
from a data set that is further than 2 standard deviations 
from the mean is at most 25%.

Edwin