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Chapter 8: Descriptive Statistics


Measures of Variability

Variability refers to how spread apart the scores of the distribution are or how much the scores vary from each other.  There are four major measures of variability, including the range, interquartile range, variance, and standard deviation.  The range represents the difference between the highest and lowest score in a distribution.  It is rarely used because it considers only the two extreme scores.  The interquartile range, on the other hand, measures the difference between the outermost scores in only the middle fifty percent of the scores.  In other words, to determine the interquartile range, the score at the 25th percentile is subtracted from the score at the 75th percentile, representing the range of the middle 50 percent of scores.

The variance is the average of the squared differences of each score from the mean.  To calculate the variance, the difference between each score and the mean is squared and then added together.  This sum is then divided by the number of scores minus one.  When the square root is taken of the variance we call this new statistic the standard deviation.  Since the variance represents the squared differences, the standard deviation represents the true differences and is therefore easier to interpret and much more commonly used.  Since the standard deviation relies on the mean of the distribution, however, it is also affected by extreme scores in a skewed distribution.



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