How to Measure Variability
Variability, Range, Interquartile, Mean Absolute Deviation (Measures of Variability)does
Variability refers to how spread scores are in a distribution out; that is, it refers to the amount of spread of the scores around the mean. For example, distributions with the same mean can have different amounts of variability or dispersion. Despite the equal means the mean score for both quizzes is 7 , the scores on Quiz 1 are more packed or clustered around the mean, whilst the scores on Quiz 2 are more spread out. Thus, the differences within the student group were greater on Quiz 2 than on Quiz 1. The most basic measure of variation is the range, which is the distance from the smallest to the largest value in a distribution. However, the range uses only two values in the data set, and one of these values may be an unusually large or small value.
Variability is the extent to which data points in a statistical distribution or data set diverge from the average value as well as the extent to which these data points differ from each other. In financial terms this is most often applied to variability of investment returns. Understanding the variability of investment returns is just as important to professional investors as understanding the value of the returns themselves. Investors equate a high variability of returns to a higher degree of risk when investing. Professional investors perceive the risk of an asset class to be directly proportional to the variability of its returns. As a result, investors demand a greater return from assets with higher variability of returns, such as stocks or commodities, than what they might expect from assets with lower variability of returns, such as Treasury bills. This difference in expectation is also know as the risk premium , The risk premium refers to the amount required to motivate investors to place their money in higher-risk assets.
Statisticians use summary measures to describe the amount of variability or spread in a set of data. The most common measures of variability are the range, the interquartile range IQR , variance, and standard deviation. If you view this web page on a different browser e. The range is the difference between the largest and smallest values in a set of values. For example, consider the following numbers: 1, 3, 4, 5, 5, 6, 7, For this set of numbers, the range would be 11 - 1 or
Variability refers to how "spread out" a group of scores is. To see what we mean by spread out, consider graphs in Figure 1. These graphs represent the scores on two quizzes. The mean score for each quiz is 7. Despite the equality of means, you can see that the distributions are quite different.
The formula is easy: it is the square root of the Variance. So now you ask, "What is the Variance? You and your friends have just measured the heights of your dogs in millimeters :. And the good thing about the Standard Deviation is that it is useful. Now we can show which heights are within one Standard Deviation mm of the Mean:.