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# Statistics Lecture 4

CJ3347-256 Spring 2013
by

## Dustin Melbardis

on 29 September 2014

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#### Transcript of Statistics Lecture 4

Description continued Measures of Variability The Concept of Variability Standard deviation (s) Computing Formulas Standard Deviation and the Normal Distribution Variability refers to how spread out or scattered the scores of a distribution are Conceptual Meanings How can one use the standard deviation? The Variance (s²) A more sophisticated measure of variability, attempts to account for all of the scores by summing the deviation of each score from the mean The Range the difference between the highest and lowest scores in a distribution. the average variability in a distribution There are several ways to get the variance and the standard deviation graphic interpretations how different the scores are how unlike the scores are from one another If we were to only report a measure of central tendency, then we would have an incomplete understanding of the distribution R = H - L Advantage: it is not computationally demanding. Disadvantage: does not consider all of the scores in the distribution 85 85 85 85 85 85 85 85 85 85 85 86 85 84 89 81 85 85 83 87 97 79 58 89 93 69 85 91 90 99 xbar = 85 R = 0 R = 8 R = 41 However, simple summation leads to the undesirable and inevitable outcome of equaling zero. To overcome this outcome, we square each deviation before summing Bessel's correction allows us to find the average of the squared deviations in the set of scores how far each case deviates from the mean, on average On average, each score differs from the mean by this amount. Some scores are close, and some are farther away, but on average, each score is this distance away from the mean. just take the square root of the variance! However, the computing formulas that your book use are only appropriate if big N is used, and we don't do that. The larger the standard deviation, the greater variability in a distribution of scores One can compare variability in different distributions Interpretations of individual scores are more detailed xbar = 75, s = 1.5 xbar = 75, s = 5
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