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    Statistics Definitions

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    In this unit, you studied several measures of central tendency. By far the most frequently utilized of these measures is the mean of a population. Remember that the source of the data that you want to analyze always comes from what is called a population. If you are interested in the average high temperature in your area for the month of July, then your population would be the 31 daily high temperatures in July, and the mean would be the total of these temperatures divided by 31.

    Now, suppose you calculate a mean of a population and you want to know how representative that mean is of a random data point in that population. In other words, is the data bunched tightly around the mean, or is it more loosely distributed over the possible range of values? An example would be high temperatures in July versus high temperatures in April or October. In general, the highs in April and October will vary more widely from the means in those months than the highs in July.

    In summary, it takes not only the mean to adequately describe a population, but there must be some way to measure the dispersion, or distribution, of the data around the mean.

    Use the Library and the Internet to research the definition of what is called the distribution of a data population. Also, find the statistic that measures the width of dispersion ("looseness" or "tightness") of the population data about its mean. Present your findings on the Discussion Board and give an example of the type of situation where this statistic might be critical to making good decisions about the population under study.

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    Solution Preview

    Please see the attached file.

    Use the Library and the Internet to research the definition of what is called the distribution of a data population.

    The distribution is a function that describes the probabilities associated with each value.

    Look at the dice example from your last posting that I answered (posting #119136). Each x value (each roll of the dice: 2 through 12) has an associated probability (I only calculated the probabilities for 2, 6, and 12, but every value from 2 to 12 has a probability).

    All distribution functions must satisfy two criteria: (1) each probability associated with each x value must be between 0 and 1, and (2) if you add all of the possible probabilities together, ...