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Week 2: Central Tendency, Variability, & z-scores: Location of Scores…
Week 2: Central Tendency, Variability, & z-scores: Location of Scores and Standardized Distributions
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Line graph:
A display in which points connected by straight lines show several different means obtained from different groups or treatment conditions. Also used to show different medians, proportions, or other sample statistics.
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Skewed distribution: the scores tend to pile up toward one end of the scale and taper off gradually at the other end.
Variability: provides a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together 
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Variability measures how well an individual scored (or group of scores) represents the entire distribution.
Provides information about how much error to expect if you are using a sample to represent a population
Range: the distance covered by the scores in a distribution, from the smallest score to the largest scores.
Standard deviation: provides a measure of the standard, or average, distance from the mean, and describes whether the scores are clustered closely around the mean or are widely scattered.
Deviation: the distance from the mean (i.e., the deviation for each score is the difference between the score and the mean.)
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Variance: the mean of the squared deviations. Variance is the average squared distance from the mean.
Population variance: represented by the symbol and equals the mean squared distance from the mean. Population variance is obtained by dividing the sum of squares by N.
Population standard deviation: represented by the symbol and equals the square root of the population variance.
Sample Variance: represented by the symbol s2 and equals the mean squared distance from the mean. Sample variance is obtained by dividing the sum of squares by n − 1.
Sample standard deviation: represented by the symbol s and equal the square root of the sample variance.
Degrees of freedom (df), for the sample variance are defined as the degrees of freedom determine the number of scores in the sample that are independent and free to vary
A sample statistic is unbiased if the average value of the statistic is equal to the population parameter.
A sample statistic is biased if the average value of the statistic either underestimates or overestimates the corresponding population parameter.
Sample standard deviation: represented by the symbol s and equal the square root of the sample variance.
z-score: specifies the exact location of each X value within a distribution. They always consist of two parts: a sign (+ or -) and a magnitude. Both are necessary to describe completely where a raw score is located within a distribution.
A standardized distribution is composed of scores that have been transformed to create predetermined values for μ
and . Standardized distributions are used to make dissimilar distributions comparable.
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