SECTION 3.3.enex

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Department
Economics
Course
ECON 202
Professor
Schultz--- Universityof Illinois
Semester
Summer

Description
SECTION 3.3: MEASURES OF DISTRIBUTION SHAPE, RELATIVE LOCATION, AND DETECTING OUTLIERS SKEWNESS: the "weight" of the data: whether or not the data is sk ewed to the right or left.      LEFT SKEW: skewness is negative, mean is smaller than median div>      RIGHT SKEW: skewness is positive, mean is greater than median      SYMMETRIC: skewness is zero, mean and median are equal< /div> Z-SCORE: also known as the "standardized value", also interp reted as the number of standard deviations from the mean.             Interpreted as a measure of the relative location of the observation in a da ta set.  CHEBYSHEV'S THEOREM: enables us to make statements about the proport ion of data values that must be within a specified number of standard deviations of the mean.       At least (1-1/z2) of the data values must be within z s tandard deviations of the mean, where z is any value greater than 1.       THEREFORE:                At least 75% of the data values must be within z=2 standard deviati s of the mean.                At least 89% of the data values must be within z=3 standard deviations of e mean.                At least 94% of the data values must be within z=4 standard deviations of e mean.  EMPIRICAL RULE: based on the normal probability distribution, used t o determine the percentage of data values that must be within a specified number of standard deviations of the mean.             For data in a bell-shaped distribution:                 Approximately 68% of the data values will be one standard deviation from t mean.                Approximately 95% of the data values will be two standard deviations from e mean.                Almost all of the data values will be within three standard deviations fro the mean.  OUTLIERS: sometimes a data set will have one or more observations wi th unusually large or unusually small values, these data points are called outli ers.       Z-scores can be used to determine outliers.  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