OBJECTIVES:
INTRODUCTION:
In all these examples one discovers that, if one repeats the observation,
the new number will differ from the preceding one. More
importantly the number found can not be predicted using the knowledge of a
preceding observation nor can it be used to predict the following one.
For example the number of babies born
on a particular Monday will usually be different from the number born on the
succeeding Monday. Similarly, the number of patients (out of a different
one thousand) that feel better after taking
a particular kind of pain reliever, or the number of murders in the
following year in New York City will be unpredictably different.
What does the figure tell you?
You may argue that the value of in the two examples was obtained using
many observations; how can one know its value if one does only one
observation?
In other words, if I make only one observation, for instance if I
find that the number of drops
in a single square is N = 35, what can I say about how far from the unknown
but true value
it is likely to be?
REQUIRED KNOWLEDGE:
If one makes a histogram of the number of times a certain count appears one
finds a bell shaped curve called a ``Gaussian distribution'' centered on
the average.
The histogram below looks a lot better than the ones you have seen above;
this is so because it shows the distribution of many more observations.
The histogram shows that counts of about 100 are most frequent, and that counts of 70, or 130 are much less likely to occur; we can think of the ``width'' of the curve i.e. the range of the counts that occur most frequently is about 20.
Statistical theory predicts that the width of the curve, the
``standard deviation'' of the distribution is defined as:
The standard deviation is a measure of how wide the curve is;
about 1/3 of the counts will lie outside the interval
-
to
+
.
Only about 1/20 of the counts will lie outside the interval
-2
to
+2
.
The value of
is calculated automatically by your computer, so you do not really have to worry about it. However here goes the formula, you may skip this if you
wish.
EXPERIMENT
EQUIPMENT
PRECAUTIONS: The Geiger counter has a very thin window to permit the entry of ![]() ![]() |
PROCEDURE I:
![]() | ![]() |
![]() |
100 x ![]() |
100 x ![]() |
mean | std. dev. | rel. unc. | ||
QUESTIONS