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-----?
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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/k^2}}}.

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 {{{1/2^2}}}.

or writing {{{4}}} for {{{2^2}}},

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 {{{1/4}}}.

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</pre>