Measures of Variability

MARY KRYSTLE DAWN D. SULLEZAReporter

CHAPTER FOUR:

VARIABILITY: the “spread” in a set of measurement.-it refers to how spread out a group of data is.

In other words, variability measures how much your scores differ from each other. Variability is also referred to as dispersion or spread. Data sets with similar values are said to have little variability, while data sets that have values that are spread out have high variability.

Imagine that you are teaching a Psychology course and you want to examine your students' performance on the midterm and final exams. The grades of your students are as follows:

At a glance, you notice that there is only one student who received the same grade for both the midterm and the final. You now want to know if the students' scores on each exam are similar to each other, or if the scores are spread out. What you are interested in is called variability.

D. THE STANDARD DEVIATION AND VARIANCE: The most widely used measure for showing the

variability of a set of scores are the Standard Deviation (s) and the Variance (s2). Some writers used σ rather than s. The s as used here will apply to statistic derived from a sample of scores drawn from a population.

VARIANCE: is the mean or average of the squares of the deviation of each measurement from the mean.

The variance cannot easily be related to the original measures from which it was obtained because all the differences from the mean were squared. A measure of variability that is compatible to the original measure is obtained by taking the square root of the variance. The result is called the Standard Deviation.

The above method of solving for the standard deviation is known as the “ deviation-score” method for ungrouped data. Another frequently used method for finding s is the “raw-score” method for ungrouped data. The formula is given below;

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