The Measures of VariabilityMeasures of variability show how spread out scores are. The range, variance, and standard deviation are common tools for viewing dispersion.If scores are very similar, they have low variability. They are homogeneous. If they are extremely dissimilar, or show a high degree of variability, they are heterogeneous. If you are a reading teacher, it is much easier to instruct a class that is grouped homogeneously because students would be have similar reading skills. Imagine how difficult it would be to teach at a Little House on the Prairie school (a one-room school house for all kids), where student reading levels within the same class vary greatly. The range is the simplest measure of variability. It is the difference between the highest and lowest score. The range is helpful, but it does not consider how closely dispersed the scores are.
Let's assume these are IQ scores: 95, 96, 100, 104, 105, 140 The range is 140-95 = 45 While the spread of scores using the range is 45, it is apparent that 5 of the 6 scores are clustered toward the low end of the range within 10 points of each other.
The variance and standard deviation are better indicators of the spread of scores because they consider every score in the calculation. If you look at the formulas, it is easy to see that the standard deviation is the square root of the variance. The standard deviation is the average spread of scores. The process for the top part of the equation, according to the formula, is to subtract each score (x) from the mean score (x-bar), square each difference, then add them all up. Scores: 95, 96, 100, 104, 105, 95-100 = -5 squared = 25 96-100 = -4 squared = 16 100-100 = 0 squared = 0 104-100 = 4 squared = 16 105-100 = 5 squared = 25 Add up the differences = 82 (top part of equation) Divide 82 by n - 1 or 82 divided by 4 The answer is 20.5. This is the variance. The standard deviation is the square root of 20.5, or 4.53
Top of Measures of Variability
|
