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 variable's 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 98 120 98 87 84 83 84 83 82 105 80 89 7994 76 107 86 107 87 If put in order and split into quartiles, the data set becomes 76 83 87 98 79 84 87 105 80 84 89 107 82 86 94 107 83 87 98 120 1st quartile = 2nd quartile (median) - 3rd quartile = 75 80 85 90 95 100 105 110 115 120 and it The minimum, 1st quartile, median, 3rd quartile, and maximum are shown in the graph above. This drawing is called a shows the data to be considerably skewed to the right. 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 variable's 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 98 120 98 87 84 83 84 83 82 105 80 89 7994 76 107 86 107 87 If put in order and split into quartiles, the data set becomes 76 83 87 98 79 84 87 105 80 84 89 107 82 86 94 107 83 87 98 120 1st quartile = 2nd quartile (median) - 3rd quartile = 75 80 85 90 95 100 105 110 115 120 and it The minimum, 1st quartile, median, 3rd quartile, and maximum are shown in the graph above. This drawing is called a shows the data to be considerably skewed to the right