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Descriptive Statistics
Involves computing summary measures and constructing graphs, tables and charts to illustrate those measures
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Measures of Location Arithmetic Mean or Average; Median; Mode; and
Weighted Average
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Measures of Variability or Spread
Range; Variance; Standard Deviation, and Coefficient of Variation
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Measures of Location Measures of location describe data by providing a central tendency (location) value for the data
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Arithmetic Mean or Average
Population: x = (Xi) / N where: x = population mean; Xi = the ith value in the data set; = summation symbol; and N = population size Sample: X = (Xi) / n where: X = sample mean; Xi = the ith value in the data set; = summation symbol; and n = sample size
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Median The median is the middle observation in data that have been arranged in ascending or descending numerical sequence Median = (n + 1) / 2 ranked observation where n = number of observations
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Mode The mode is the value in a set of data that appears most frequently
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Weighted Average A weighted average is an arithmetic mean for which each value (X) is weighted (W) according to some well-defined criterion Xw = (XW) / W
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Measures of Variability or Spread
Measures of variability or spread describe data by indicating the extent of the differences between the values of a data set
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Range The range of the data set is the difference between the largest and smallest values in the set Range = Largest Value - Smallest Value
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Variance x2 = ( Xi - x )2 / N for populations
The variance provides a numerical measure of how the data tend to vary around the arithmetic mean x2 = ( Xi - x )2 / N for populations s2 = ( Xi - X )2 / (n - 1) for samples
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Standard Deviation The standard deviation may be thought of as a measure of distance from the mean STD = SQRT of Variance Population: Sample: = SQRT OF 2 S = SQRT of S2
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Coefficient of Variation
The coefficient of variation is a measure of relative variation Population: Sample: V = ( / x ) * 100 V = ( S / X ) * 100 where: V = Coefficient of Variation
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