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VARIABILITY
provides a quantitative measure of the differences between…
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.
The median and interquartile range are presented in a graph called a BOXPLOT. A box plot also includes the range of scores from the minimum X to maximum X values.
The FOUR MEASURES OF VARIABILITY are
range, IQR, standard deviation, and variance.
DEGREES OF FREEDOM (df) determine the number of scores in the sample that are independent and free to vary.
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VARIANCE equals the mean of the squared deviations. Variance is the average squared distance from the mean.
MEAN SQUARE (MS), is often used to refer to variance, which is the mean squared deviation.
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POPULATION VARIANCE
is represented by the symbol and equals the
mean squared distance from the mean.
Population variance is obtained by
dividing the sum of squares (SS) by N.
STANDARD DEVIATION uses the mean of the distribution as a reference point and measures variability by considering the distance between each score and the mean.
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POPULATION STANDARD DEVIATION is represented by the symbol and equals the square root of the population variance.
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RANGE is the distance covered by the scores in a distribution, from the smallest to the largest score.
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A sample statistic is unbiased if the average value of the statistic is equal to the population parameter.
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the average of all the sample variances will produce an accurate estimate of the population variance.
A sample statistic is biased if the average value of the statistic either underestimates or overestimates the corresponding population parameter.
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The symbol Σ (the Greek letter, "Sigma") means “sum of,” while (X-μ) is a deviation (the difference between a score, X, and the mean, μ). Thus, you have the sum of the squared deviations.
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To calculate the Sum of Squares using the definitional formula, follow these steps:
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