Medians and Means
Although the inflation-adjusted long-term distributions show that prices spend much more time at lower levels, there is a tendency to consider the average price of a market as the midpoint between the highest and lowest prices. Using the gold example, the midpoint for 1979 to 1993 was $451. The average of all monthly prices will give a reasonable approximation of a normal price; however, the best measure is the median, or middle, value when all monthly prices are sorted from high to low. The median value for gold over the same period was $381. If we look back at earlier posts we find that skewness is measured as the difference between the mean and the median, as a percentage of the standard deviation. In this case, the difference of $70 is a very large value, indicating a distribution with a peak far to the left of center. For price distributions, the median is a much more useful value than the average, although not as convenient to calculate. The median naturally adjusts for the skewness in the price patterns.
USE OF PRICE DISTRIBUTIONS AND PATTERNS TO ANTICIPATE MOVES
Prices often form patterns that can be evaluated using probability methods, or simply viewed in much the same way as a frequency distribution, or histogram. Because the concepts are sound, but the statistical analysis is often difficult because of limited amounts of data or changing conditions, analysts have taken a much more empirical approach toward studying price distributions. The following section will look at some innovative ways to look at price distributions and how they are interpreted into trading opportunities.