ThE hAnDbook of TEChnICAl AnAlysIsOne way to quantify these deviations is to assume that the empirical data
distribution corresponds closely to a normal distribution. This is very helpful as
the normal distribution has various properties that one may use as a basis for fore-
casting potential overreactions or statistically significant prices, returns, or related
events in the markets. The closer an empirically derived distribution of price or
other data is to a normal distribution, the more we may use the normal distribu-
tion as a proxy for the original distribution. The central limit theorem states that
with sufficient independent and identically distributed random variables, the dis-
tribution begins to approximate a normal distribution. This is important, as it al-
lows many empirical observations to assume the useful characteristics of a normal
distribution. A normal distribution has the following characteristics:
■ (^) The mean, mode, and median have the same values
■ (^) It has a symmetrical distribution
■ (^) 68.2 percent of the values lie between ± 1SD
■ (^) 95.4 percent of the values lie between ± 2SD
■ (^) 99.7 percent of the values lie between ± 3SD
The last three dispersion characteristics are by far the most useful properties
of a normal distribution. Useful and effective forecasts may be made based on
dispersion statistics such as these. See Figure 21.15.
The mean, mode, and median are all measures of central tendency where:
■ (^) The mean represents the average of all data
■ (^) The mode represents the most frequently recurring data
■ (^) The median represents the middle of all data
A very rudimentary test of how well our data approximates to a normal distri-
bution may be determined by the amount of discrepancy between the values of the
mean, mode, and median. In a normal distribution, all three measures of central
tendency have the same value.
figure 21.15 The Normal Distribution Dispersion Characteristics.