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Other Measures of Spread

The range , calculated as $R=\mbox{Max}-\mbox{Min}$, is sometimes used as measure of spread  instead of the SD. It does not have mathematical properties like the empirical rule, but it is quick and easy to compute, and easier to understand. When monitoring manufacturing processes (like the amount of fill in a soda bottle), the range is often used to monitor whether the process needs adjustment. A relatively large range means that the filling process is inconsistent.

The coefficient of variation  is the SD divided by the average (CV = $S/\overline{X}$). Suppose that the daily closing stock price for IBM during the past month averaged $120 with SD $12, while Dell Computers averaged $30 with SD $6. It may seem that the price for IBM is more variable because the SD is larger; however its SD is only 10% of its average stock price (CV = $12/$120 = .10) while Dell's SD is 20% of its average stock price (CV = $6/$30 = .20). If you want to measure price volatility, do you prefer the SD or the CV?


next up previous contents index
Next: Adding a Constant Up: Location and Spread Previous: Other Measures of Location

2003-09-08