PS296 Week 2C (Measures of Variability)
• Also called measures of dispersion.
• Indicate how spread out (dispersed) the scores in a distribution are.
• Dispersion (Variability):
– the degree to which individual data points are distributed around the mean
• All yield numerical values, i.e., a quantification of variability.
Measures of variability
• Sum of squares
• Standard deviation
Range: Calculated as the difference between the highest score and the lowest score in a data set.
• Range = (Highest score - Lowest score)
• advantage: simple to calculate
• disadvantage: takes into account only two scores, no matter how large your data set
• so, it is sensitive to all scores
• how much each score varies (deviates) from the mean
• involves deviation scores:
deviation score = (x-x)
• problem: sum of the deviation scores in a data set always equals 0 (within rounding error), i.e.,
Σ(X - X) = 0
• So the average deviation score also always equals 0
Mean absolute deviation
• MAD = • Not difficult to calculate, but doesn’t have the nice statistical properties that other measures of
• Rather than use the absolute deviation, another way of getting rid of the negative values is to
square each deviation score.
Sum of squares
• SS = the sum of the squared deviation scores
• SS = Σ(X - X)
– Calculate the mean: X
– Calculate the deviation scores: (X – X)
– square each deviation score: (X - X) 2
– Sum the squared deviation scores: Σ(X - X)
• variance is like an average squared deviation.