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Measure of Variability
 Measures of variability describe the extent
 to which scores in a distribution differ from each other

The Range
 The range indicates the distance
 between the two most extreme scores in a distribution

Variance and Standard Deviation
 two measures of variability that indicate
 how much the scores are spread out around the mean
 •We use the mean as our reference point since
 it is at the center of the distribution

SampleVariance
/ Sample Standard Deviation
 sample variance is the average of the squared deviations of
 scores around the sample mean
Formula:


Population Variance
Formula

Population Standard Deviation
Formula

Estimated Population Variance
 By dividing the numerator of the sample
 variance by N  1, we have an unbiased
 estimator of the population variance


Estimated Population Variance
Computational formula

Estimated Population Standard Deviation
 By dividing the numerator of the sample
 standard deviation by N  1, we have an unbiased
 estimator of the population standard deviation.
Formula

Unbiased Estimators
 1.
 2.
 Quantity N1 is called the degrees of freedom

Proportion of Variance Accounted For
 proportion of variance accounted for is the proportion of
 error in our predictions when we use the overall mean to predict scores that is eliminated when we use the relationship with another variable to predict scores