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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:
Computational 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
Formula:
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 N-1 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