PS296 Lecture Notes - Lecture 3: Squared Deviations From The Mean, Variance
Variance:
-measures or index of the amount of variability in a dataset
-presented in squared units
-sample variance is the sum of the squared deviations about the sample mean (xbar) divided by
the sample size (n) – 1
-deviation from the mean: the difference between each score and the mean of the distribution
-n – 1 = the total number of scores minus 1 (lowercase n for sample)
The following formulas are used to calculate the sample variance (s²)
small sigma² = population variance (circle with a line over it σ)
s² = sample variance
x – xbar = the deviation, it is the single score minus the average
-sx² is the summation
-the other half is the deviation from the mean
-SS = sum of squares, sum of the squared deviations
1) calculate the mean
2) calculate the deviation scores
Document Summary
Measures or index of the amount of variability in a dataset. Sample variance is the sum of the squared deviations about the sample mean (xbar) divided by the sample size (n) 1. Deviation from the mean: the difference between each score and the mean of the distribution. N 1 = the total number of scores minus 1 (lowercase n for sample) The other half is the deviation from the mean. Ss = sum of squares, sum of the squared deviations: calculate the mean, calculate the deviation scores, square each score, add up the values x x xbar x - xbar . Sigma(x-xbar) = 10 xbar 20 divided by 5 = 4 if correct, this should be 0. The mean is 4 deviation scores this is the numerator. Sx = 10 divided by (5-1) = 10 divided by 4 = 2. 5. Interpretation: the scores in our sample deviated an average of 2. 5 squared units from the mean.
