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18. Measures of Dispersion Suppose two stocks have the same mean expected return (10%). However, one stock always has a 10% return, while the other

18. Measures of Dispersion

Suppose two stocks have the same mean expected return (10%). However, one stock always has a 10% return, while the other stock is very unpredictable. Which one would you want? Probably the first one, right? This section defines some basic measures of dispersion, also known as spread or variability, and how they help interpret data.

Range

The simplest measure of dispersion is range, which is defined as the span of values that a variable takes. You can find the range by determining the difference between the maximum and minimum values, as follows:

Range = Maximum Value Minimum Value

The range is useful because it is easy to calculate and even easier to understand.

Comparing the range and the mean indicates how significant the dispersion is. However, the range does not measure the dispersion of the majority of the observations; it focuses only on the highest and lowest values. Therefore, it is very sensitive to outliers.

Consider the following two 10-item data sets:

Data Set A

12, 12, 12, 13, 13, 14, 22, 23, 23, 24

Data Set B

124, 126, 127, 129, 129, 130, 132, 132, 133, 136

Both data sets have a range of but they certainly are not dispersed the same.

Quartiles

The range shows the minimum and maximum values, and the median shows the middle value. If you combine the range and the median, the picture of a variables distribution starts to come into focus. This process can be taken a step further by calculating quartiles and plotting the data.

Consider this data set:

87 120 87 84 83 105 80 89 107 107
98 98 84 83 82 79 94 76 86 87

If put in order and split into quartiles, the data set becomes

76 79 80 82 83
83 84 84 86 87
87 87 89 94 98
98 105 107 107 120
1st quartile = ______
2nd quartile (median) = ______
3rd quartile = _______

The minimum, 1st quartile, median, 3rd quartile, and maximum are shown in the graph above. This drawing is called a _________ and it shows the data to be considerably skewed to the right.

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