 |  Behavioral Statistics in Action, 3/e Mark W. Vernoy,
Palomar College
Diana J. Kyle,
Fullerton College
Measures Of Variability
Glossary
| Average mean deviation (AMD) | is the average deviation of each deviation score from the mean of the distribution. To compute the average mean deviation, the mean is subtracted from each score to arrive at the deviation scores. The deviation scores are summed and then divided by the total number of scores. Since about half of the deviation scores are positive for the scores larger than the mean and the other half are negative for scores smaller than the mean, the average mean deviation always equals zero. Thus, it cannot be used for any meaningful comparisons between different distributions.  <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0767422759/35691/gloss5_1.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (3.0K)</a>]]>
| | | | | Measures of variability | indicate how much scores in a distribution vary either from the mean or the full extent of the distribution. It is the spread of all the scores in a distribution. Four measures of variability are discussed in this chapter: the range, the average mean deviation, the variance, and the standard deviation. These measures of variability can reveal the consistency or similarity of the scores in a distribution and the extent the mean truly represents all of the scores in the distribution.
| | | | | Standard deviation | is represent by either <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0767422759/35691/q.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>]]> (population) or  <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0767422759/35691/S.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>]]> (sample). The standard deviation is the square root of the variance. It represents the average amount each score in the distribution deviates from the mean. It is expressed in the same units as the original scores and indicates the consistency or similarity of the scores in a distribution and the extent the mean truly represents all of the scores in the distribution. <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0767422759/35691/gloss5_3.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>]]>
| | | | | The range | is a measure of the full extent of how far the scores are spread out in a distribution from the highest to the lowest. It is the easiest of the measures of variability to compute, but it is seldom used because of its instability. One extreme score can drastically alter the range. Range = high score - low score.
| | | | | Variance | is represented by either  <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0767422759/35691/q2.gif','popWin', 'width=35,height=33,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>]]> (population) or  <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0767422759/35691/S2.gif','popWin', 'width=33,height=33,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>]]> (sample). Variance is computed from deviation scores that are squared to remove the positive and negative signs. The mean of the squared deviation scores is called the variance.
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2002 McGraw-Hill Higher Education