•One Die

Here are the possible outcomes from the roll of a single die.  Each outcome is equally likely.  This is our population.

In[8]:=

oneDice = {1, 2, 3, 4, 5, 6} ;

What is the mean of this population?

In[65]:=

μ1 = Mean[oneDice] // N

Out[65]=

3.5`

In[19]:=

Tr[oneDice]/Length[oneDice]

Out[19]=

7/2

In[60]:=

σ1 = StandardDeviationMLE[oneDice] // N

Out[60]=

1.707825127659933`

In[61]:=

s1 = StandardDeviation[oneDice] // N

Out[61]=

1.8708286933869707`

In[31]:=

Histogram[oneDice]

[Graphics:../HTMLFiles/DiceStats_12.gif]

Out[31]=

-Graphics -

Is that last graph lying with statistics or what?  Here's a more complicated way of asking for that, specifying that the counting is to be done in bins that are 1 wide from 0.5 to 6.5.

In[37]:=

Histogram[BinCounts[oneDice, {0.5, 6.5, 1}], FrequencyData -> True]

[Graphics:../HTMLFiles/DiceStats_15.gif]

Out[37]=

-Graphics -

Converted by Mathematica  (September 11, 2003)