Measurement and Statistics_Dasch_Date__021510

# Measurement and Statistics_Dasch_Date__021510 - Statistics...

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Statistics Basics Total Error = Sum of Deviances SUM(x i – mean) Example: 10 8 8 9 5 mean = 8 10 – 8 =2 8 – 8 = 0 8 – 8 = 0 9 – 8 = 1 5 – 8 = - 3 SUM = 0 Sum of deviances is always equal to 0 Since this is not a good measure of variability, must do sum of squared errors Sum of Squared Errors Also referred to as SS SUM(x i – mean) 2 example: using same numbers 10 – 8 = 2 2 = 4 8 – 8 = 0 2 = 0 8 – 8 =0 2 = 0 9 – 8 =1 2 = 1 5 – 8 = 3 2 =9 SUM = 14 good measure of accuracy, but it is dependent upon the size of the data set must control for size of data set

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Variance SS/ (N-1) Example: 14/4 = 3.5 units squared Gives answer in units squared (N-1) = degrees of freedom Standard Deviation SQUARE ROOT(variance) = SQUARE ROOT(SS/(N-1) Example: SQUARE ROOT(3.5) = 1.87 Defines the measure of variation in a given data set The smaller the standard deviation, the more accurate the mean is
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Measurement and Statistics_Dasch_Date__021510 - Statistics...

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