sess2 - Session 2: Frequency Distributions and Probability...

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Session 2: Frequency Distributions and Probability Theory BUS 501: Quantitative Methods for Business

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Probability and Frequency Distributions A relative frequency distribution describes the percentage of the population of values, that belongs to a particular value in the data population. It also tells us the probability of observing a particular value in this data population: If you randomly draw one observation from a population of size N, then the chance of drawing each member of that population is 1/N; But since the frequency of a particular value appearing in the population is f , then the chances of that value being the one observed will be f *(1/N) or f /N, its relative frequency. A relative frequency distribution function is one of the ways by which the probability distribution function describing the chance of observing a random variable may be derived. Note that much as a relative frequency distribution means that the ∑(f(x i )/N) = 1.0 for i from 1 to N, the ∑p(x i ) = 1.0 for i from 1 to N.
Example Using the same population of letter grades for a class of five students we had earlier (X 1 = A, X 2 = B, X 3 = C, X 4 = B, X 5 = B): the probability of observing a letter grade of A in this class is 1/5, which is also the relative frequency of A in the set of 5 data observations, the probability of observing a letter grade of B is 3*(1/5) = 3/5, and the probability of observing a letter grade of C is 1/5, the probability of observing A, B or C is P(A) + P(B) + P(C) = 1.0 .

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Probability Probability is a numerical measure of the chances (likelihood) of observing an event happen. When we make a decision, the outcome from that decision may take the form of many possibilities - the simplest example may that be of success or failure. If that decision can be repeated several times, we can observe the frequency of successes and the frequency of failures and use the relative frequencies of these observations to assign probabilities to success and to failure. For example, if we toss a coin several times, there are only two possibilities - it will either show a Head (man’s head) or a Tail (not a man’s head). If we observe Head appearing 60% of the time, then the relative frequency of observing Tail must be 40%. We can then assign 60% as the probability that a Head will show when we flip a coin, and 40% to the possibility of a Tail.
Probabilities The relative frequency method (from experimentation) is only one way by which we can assign probabilities, other methods are: The so-called classical method by which we automatically assume equal probabilities to mutually exclusive, but exhaustive outcomes for which we have no reason to believe that one outcome is more likely to happen than the other. Another method is called the subjective method

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This note was uploaded on 05/20/2010 for the course MGT 450 taught by Professor Mandeepsingh during the Spring '10 term at Punjab Engineering College.

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sess2 - Session 2: Frequency Distributions and Probability...

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