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# Variability & Range Psyc-21621

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This 2 page Class Notes was uploaded by Amy Turk on Wednesday April 27, 2016. The Class Notes belongs to Psyc-21621 at Kent State University taught by Dr. Gordon in Spring 2016. Since its upload, it has received 4 views. For similar materials see Quantitative Methods Psych I in Psychlogy at Kent State University.

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Date Created: 04/27/16

PSYCH STATS POWERPOINT 4 ● Variability: how scores are spread out in a distribution ○ more scores, greater variability ○ a lot of deviation and different values ○ a measure of how spread out or close together a set of scores are within a distribution ○ refers to the distance between scores ○ can also refer to individual scores ■ how far away from the mean is a certain score? ○ small, large, or none ○ how accurate an individual score or sample represents the entire population ○ if a score is equal to the mean, there is no variability ○ if a score does not equal the mean, we can determine the amount of variability that exists ● matters for descriptive stats ○ describes a facet of the entire distribution ○ visualize the distribution with central tendency and variability ○ how well a group of scores represents a distribution ● useful for inferential stats ○ how well an individual score represents an entire population ■ info on how much error we should expect if we use a sample to represent a population ● when the population variability is small, the scores are close together ○ any individual score or sample will likely be a good representation of the population ● when variability is large, the scores are not a good representation of the population ● selecting a participant from a distribution with a lot of variability can lead to error Measures ● range: distance between largest and smallest scores ● interquartile range: the range covered by the middle 50% of the distribution ● standard deviation: measures the standard distance between a score and a mean ● interval or ratio data only Range ● subtract the largest score by the smallest score ● does not consider all scores ○ unreliable ● influenced heavily by outliers ● the 68-95-99.7 Rule ● interquartile range: to avoid extreme scores you can use the interquartile range ○ looks at the middle 50% of the distribution ○ first need to locate the boundary that seperates the lower 25% and the top 25% ● range and interquartile range ○ only provides a crude measure of variability ○ provides no info on shape ○ interquartile range disregards lots of data ● deviation ○ distance from the mean ○ score minus the mean ○ deviation score gives us a number and direction for each score ● standard deviation ○ approximate average distance from the mean ○ commonly noted as SD ○ each individual score can have x numbers of SDs above or below the mean ○ steps: ■ calculate the deviance scores ● calculate the mean ■ calculate the sum of squares ● square each deviation score ■ calculate the variance ● divide the sum of squared deviation scores by N (or n - 1) for samples ■ compute the standard deviation ● take the square root of the variance to get the SD ● deviation scores should always add up to zero ○ the mean is the balance point… same number of scores above and below the mean ● step 1: find deviation ○ deviation squared ○ find average of deviation squared (variance) ○ square root of the variance = SD ● deviance: take the scores and subtract the mean from them ● standard deviation tells us the average of how far scores are from the mean

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