Today’s Question. In some data sets the scores are tightly clustered around the mean. In other data sets, the scores are spread out. How can we quantify this property of distributions?. Measures of Spread. What is spread or dispersion? The degree to which scores are clumped around the mean.
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(often called “deviation scores”)
Note the similarity to the standard formula for the mean:
Problem: The deviations from the mean sum to zero. (We proved this previously.) Recall that the deviations sum to zero because the mean is a “balancing point” for a set of scores--the point at which the “weight” of the scores above counterbalances the “weight” of the scores below.
Average Absolute Deviation: How far the typical (i.e., average) score is from the mean.
Variance: The average squared deviation score.
A third solution: Take the square root of the average of the squared deviation scores
Standard deviation: The square root of the average squared deviation score
In our example, the square root of 7 is 2.65. The standard deviation is the square root of the variance.
*** What does this tell us? It tells us how far people are from the mean, on average. (Ignoring whether people are above or below the mean.)