Thursday, 23 February 2017

What are Measures of Variability?

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Measures of variability are also called the measures of spread or dispersion. It lets the researcher know how scattered the scores are from their central tendency.

For example, if a group is homogeneous (containing individuals of nearly the same ability), most of its scores will fall around the same point on the scale; therefore, the range will be relatively short and the variability will be small.

But, if the group is heterogeneous (having individuals of widely differing capacities), scores will be strung out from high to low; thus, the range will be relatively wide and the variability will be large.

In order to indicate the variability or dispersion, the following four measures have been devised. These are:

1.    Range: It is the simplest form of measures of variability. It is the difference between the highest and the lowest scores in a distribution. Range is the crudest form of variability as it considers the extremes scores only. It is not a stable statistic (unreliable) because its value can differ from sample to sample drawn from the same population.

2.    Quartile Deviation: The quartile deviation (generally represented by “Q”) is one-half of the scale distance between the third quartile (75th percentile) and the first quartile (25th percentile) in a frequency distribution. First quartile is a point below which 25 percent of the scores lie, while the third quartile refers to the point below which 75 percent of the scores lie. Quartile Deviation (QD) is preferred when scores are widely dispersed or scattered.

3.  Average Deviation: It is also called “Mean Deviation”. It refers to the average of deviation of all scores from their mean. It does not consider signs (negative and positive) of the scores; that is, all deviation whether plus or minus are treated as positive.

4.     Standard Deviation: Standard Deviation (SD) is the square root of variance. It is the most stable form of measures of variability. It is employed in experimental work. Variance refers to the average of the square deviations of the measures or scores from their mean. Standard Deviation (SD) is used when scores are not widely dispersed or scattered.