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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.
RANGE: the distance covered by the scores in a distribution, from the smallest to the largest score
RANGE: can ALSO be defined as the difference between the upper real limit (URL) for the largest score and the lower real limit (LRL) for the smallest score
QUARTILES: a type of percentile rank, one-fourth of the distribution
INTERQUARTILE RANGE (IQR): the distance between the 25th and 75th percentile, or between Q1 and Q3
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WHEN TO USE IQR: interquartile range typically is used when measuring central tendency with the median. Both measures are related to percentiles
BOX PLOT: median and interquartile range are often presented in a graph called a box plot. A basic box plot also includes the range of scores from the minimum X to maximum X values
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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VARIANCE: equals the mean of the squared deviations. Variance is the average squared distance from the mean.
SS, or SUM OF SQUARES: the sum of the squared deviation scores.
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MEAN SQUARE: often used to refer to variance, which is the mean squared deviation
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 (SS) by N.
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DEGREES OF FREEDOM: determine the number of scores in the sample that are independent and free to vary: df = n-1
TRANSFORMATIONS OF SCALE: a set of scores is transformed by adding a constant to each score or by multiplying each score by a constant value
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MULTIPLYING: multiplying each score by a constant causes the standard deviation to be multiplied by the same constant.
BIASED STATISTIC: A sample statistic is said to be biased if, on average, it consistently overestimates or underestimates the corresponding population parameter.
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SAMPLE STATISTIC:a numerical value calculated from a subset (a sample) of a larger group (a population). It can be biased or un-biased.
UNBIASED STATISTIC: if the average value of the statistic is equal to the population parameter. (The average value of the statistic is obtained from all the possible samples for a specific sample size, n.)