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Summary statistics of numeric variables
The following table shows additional notation used in the remainder of this topic except where stated otherwise.
Notation
Description
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Value of the variable for case i
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Weight for case i
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Number of cases
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Sum of the weights for the first i cases
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Mean for the first i cases
Calculating the cell contents that are dependent on a numeric variable
The following table provides the formulas used by UNICOM Intelligence Reporter to calculate the cell contents that are dependent on a numeric variable, with the exception of percentiles: see Percentile.
Item
Formula
Mean
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Sum
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Minimum
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Maximum
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Range
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Mode
Value of X j that has the largest observed frequency. If there are several modes, the first one encountered in the data is selected.
Median
The median is the 50th percentile. See Percentile.
Variance
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Standard Deviation
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Standard Error
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Percentile
UNICOM Intelligence Reporter uses one method for computation of percentiles. Let
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where p is the requested percentile divided by 100, and k 1 and k 2 satisfy
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Then
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Let x be the pth percentile; the definition is as follows:
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Notes
Quantum uses the Aempirical (Empirical Distribution Function with Averaging) formula to calculate median. The expression is:
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See also
Formulas for cell contents