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Standard Deviation

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Standard deviation is a statistical term that provides a good indication of volatility. It measures how widely values (closing prices for instance) are dispersed from the average. Dispersion is the difference between the actual value (closing price) and the average value (mean closing price). The larger the difference between the closing prices and the average price, the higher the standard deviation will be and the higher the volatility. The closer the closing prices are to the average price, the lower the standard deviation and the lower the volatility.

Calculation

The steps for calculating a 20-period standard deviation are as follows:

  1. Calculate the simple average (mean) of the closing price. i.e., Sum the last 20 closing prices and divide by 20.
  2. For each period, subtract the average closing price from the actual closing price. This gives us the deviation for each period.
  3. Square each period's deviation.
  4. Sum the squared deviations.
  5. Divide the sum of the squared deviations by the number of periods (20 in our example below).
  6. The standard deviation is then equal to the square root of that number.

Standard Deviation Table

The 20-period standard deviation for the data above is 6.787. Note that this is the "full population" version of the Standard Deviation. There is a different kind of Standard Deviation calculation that is used when you are taking a statistical sample of a population, but that version is not used in technical analysis since all of the data points are known.

Parameters

  • Period (20) - the number of bars on the chart

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