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Thus, the standard deviation would be √
, meaning that, on average, we would
expect the die value to deviate by 1.708, or nearly 2 units from the average (1.5 to 5.5, which is
pretty much 1 to 6).
Thus, we have that:
In reality, keep in mind that we would often not know much about our population. We get the
luxury of studying something we can fully explain. This is all in an effort to better understand
sampling distributions.
Suppose we conducted an experiment of rolling the die 10 times. For one random sequence, we
might obtain the following result:
4 6
3 4
4 1
3 4
1 2
Not surprisingly, we get a fairly even spread of values 1 – 6. If we are to compute the average,
we would obtain 3.2. That is if all rolls came up as the same number, each roll would be 3.2.
Suppose we asked 19 other people to roll a die 10 times and to then report back to us the mean.
Here is what we might find (based on a computer simulation of rolls):
Statistics for Decision-Making in Business © Milos Podmanik Page 183