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 25^{th}
percentile is subtracted from the score at the 75^{th}
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.
