•σ vs sComparison

In[57]:=

σ[x_] := StandardDeviationMLE[x] ; s[x_] := StandardDeviation[x] ;

In[55]:=

t = {90., 80., 85., 85.} ;

Now find σ and s for the list t.  Make sure you understand the difference: the first is the standard deviation of that population of values.  The second is the best guess for what the standard deviation is for some large population of which t is a sample.  The second one is bigger because we had to guess the mean of the population from the mean of the sample, which makes the result more uncertain.

In[59]:=

{σ[t], s[t]}

Out[59]=

{3.5355339059327378`, 4.08248290463863`}

Converted by Mathematica  (September 11, 2003)