STATISTICS
Higher Concepts of Mathematics
The significance of a normal distribution existing in a series of measurements is two fold. First,
it explains why such measurements tend to possess a normal distribution; and second, it provides
a valid basis for statistical inference. Many estimators and decision makers that are used to make
inferences about large numbers of data, are really sums or averages of those measurements.
When these measurements are taken, especially if a large number of them exist, confidence can
be gained in the values, if these values form a bell-shaped curve when plotted on a distribution
basis.
Probability
If E1 is the number of heads, and E2 is the number of tails, E1/(E1 + E2) is an experimental
determination of the probability of heads resulting when a coin is flipped.
P(El) = n/N
By definition, the probability of an event must be greater than or equal to 0, and less than or
equal to l. In addition, the sum of the probabilities of all outcomes over the entire "event" must
add to equal l. For example, the probability of heads in a flip of a coin is 50%, the probability
of tails is 50%. If we assume these are the only two possible outcomes, 50% + 50%, the two
outcomes, equals 100%, or 1.
The concept of probability is used in statistics when considering the reliability of the data or the
measuring device, or in the correctness of a decision. To have confidence in the values measured
or decisions made, one must have an assurance that the probability is high of the measurement
being true, or the decision being correct.
To calculate the probability of an event, the number of successes (s), and failures (f), must be
determined. Once this is determined, the probability of the success can be calculated by:
p
s
s
f
where
s + f = n = number of tries.
Example:
Using a die, what is the probability of rolling a three on the first try?
MA-05
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