November 2, 2009
Statistics Notes — Mean, Variance, and Standard Deviation of a Probability Distribution
A probability distribution can be thought of as a relative frequency distribution based on a very large n. Thus, it has a mean and a standard deviation.
The mean of a probability distribution is often called the expected value of the distribution. This terminology reflects the idea that the mean represents a “central point” or “cluster point” for the entire distribution. Of course, the mean or expected value is an average value, and it is usually not a point of the sample space.
The mean, the variance, and the standard deviation of a discrete population probability distribution are found by using these formulas:
where x is the value of a random variable, P(x) is the probability of that variable.
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Example. Are we influenced to buy a product by an ad we saw on TV?
National Infomercial Marketing Association determined the number of times buyers of a product watched a TV infomercial before purchasing the product. The results are shown here:
We can treat the information shown as an estimate of the probability distribution because the events are mutually exclusive and the sum of the percentages is 100%. Compute the mean and standard deviation of the distribution.
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