18. Measures of Dispersion Suppose two stocks have the same mean expected return (10\%). However, one stock atways 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 calcutate 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 if very sensitive to outliers. Consider the following twa 10 -item dsta sets: Both data sets have a range of but they certainly are not dispersed the same. Quartiles The range shaws the minimum and maximum values, and the median shows the middle value, if you combine the range and the medlan, 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: If put in order and split into quartites, the data set becomes The minimum, ist quartile, median, Jrd quartile, and maximum are shown in the graph above. This drawing is called a shows the data to be considerably skewed ta the right