The Handbook of Technical Analysis + Test Bank_ The Practitioner\'s Comprehensive Guide to Technical Analysis ( PDFDrive )

ThE hAnDbook of TEChnICAl AnAlysIs

Calculating Mean deviation and standard deviation
Values and Their direct relationship to the first
Measure of Volatility

We use standard deviation values when we want to gauge the degree of dispersion
in terms of known percentages from the mean, for example, 68.2 percent, 95.4
percent, 99.7 percent, and so on. We use mean deviation if we want to know the
exact average dispersion values from the mean. Both standard and mean devia-
tions render the same values when the dispersion is zero.

example 1: Calculating deviation Values for increasing rates of Change in
price Assume that we have a population of prices comprising a parabolic rise in
price over a 10‐hour period at an increasing rate of $2, $4, $6, $8, $10, $12, $14,
$16, $18, and $20 per hour, respectively.

Mean rate of increase per hour

=+++++++++==($ $ $ $ $ $ $ $ $ $ )/ $ / $ 2 4 6 8 10 12 14 16 18 20 10 110 10 11

Mean Deviation is calculated as follows. We find the average of the differences
in absolute values from the mean for each value:

| $ $ | $

| $ $ | $

| $ $ | $

| $ $ | $

| $ $ | $

| $

2 11 9

4 11 7

6 11 5

8 11 3

10 11 1

−=

−=

−=

−=

−=

112 11 1

14 11 3

16 11 5

18 11 7

20 11

−=

−=

−=

−=

−=

$ | $

| $ $ | $

| $ $ | $

| $ $ | $

| $ $ | $99

9 7 5 3 1 1 3 5 7 9 10 50 10

Mean Deviation

=+++++++++=($ $ $ $ $ $ $ $ $ $ ) / $ /

==$5 per hour

Standard Deviation is calculated as follows. We find the square root of the
average squared difference in values from the mean for each value: