Other Measures of Spread

The *range* , calculated as
,
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 =
). 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?