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Hand-out%203 - change from sample to sample Sample...

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Measures of central tendency for sample data or “the three m statistics” Preliminary note In physics, there is one center of gravity for each object. In statistics, there may be up to three centers for the same sample of data. As we shall see, if some condition is satisfied by the sample distribution (*), the three centers will coincide. Note The sample mode exists for any type of sample data (qualitative or quantitative). The sample median may exist for qualitative sample data, and always exists for quantitative sample data. The sample mean is restricted to quantitative sample data. (*) The condition is twofold: the sample distribution is symmetrical and it has one and only one mode. Key note The sample mode, the sample median and the sample mean are sample statistics, and as such, their value is susceptible to
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Unformatted text preview: change from sample to sample: Sample statistics are random variables ! Measures of dispersion for sample data Preliminary note In physics, the moment of inertia is calculated by using the center of gravity of the object as point of reference. In statistics, the most used measure of dispersion for sample data (i.e., the sample variance) is evaluated by using the sample mean as point of reference. Note By definition, (1) The sample variance is non-negative. (2) The sample standard deviation is expressed in the same unit as the sample mean and the random variable of interest. (3) The coefficient of variation allows one to compare the dispersion of ‘apples and oranges’ = samples of data collected for two random variables expressed in different units or samples of data with very different means....
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