There are hundreds of known "distribution types"
which describe the "shape" of a population. You
could spend a lifetime just gathering the known
information together, let alone learning any of it. The
principal task is to calculate areas under these
curves. We will look at only 2:- The triangular distribution(for illustration).
- The "Normal distribution" (because it is important).
Suppose we had a distribution that was triangle shaped like this:
Remember that "µ" is the true average of this population. We would like to have a table showing "how close" the items in the population are to the mean. Two problems arise. First, it would depend on the
units used. You would need a different table for
acres vs. hectares vs. square miles, etc. Second, the
What proportion of the population lies within ± one
base unit from the mean? Clearly, 100%. How
about ± 0.5 base units on each side of the mean? A
bit of math (there are people to do this for us)
would tell us 75%. How about ± 0.25 of our base
unit? 21.875% is the answer. We now have a short
table we can use on
The base unit is clearly equal to "30 grebs"
(whatever that is - but it doesn't How much of the population is between 115 and 130? Half of the 25% on the "outside" of the 85-115 range, or 12½% (the other 12½% is between 70-85). We have now "standardized" all the possible bases
of triangular distributions into . | Think about that, and maybe read the previous
section again until it makes sense to you. If you
follow that idea, you can easily understand standard
deviation, confidence intervals, Z tables and a
number of other statistical ideas. It is not a difficult
concept. Now to the
This distribution never gets down to the horizontal
axis (although it gets very close) so it goes on
When applied to a population it is called "the
It doesn't matter how you calculate it, but how you
use it. Want to know how much of a normal curve
is between ±1 standard deviation? Look it up in the
table, and you get 68%. What table? Well, some
nice person has done all the math and called it a
Z-table which can be found in most statistics books.
You use it just like we did the triangular distribution
table to find the probability of any zone under the
curve or to create "confidence intervals", usually
around the mean. How do you So much for the good news. Now for the bad
news. Almost Now for the very, Next time we will talk about how to use this idea to describe the precision of a cruise. |