# Formula for Standard Deviation in Forex Trading: A Guide

## Understanding Standard Deviation as a Volatility Measure

Standard deviation is one of the most widely used indicators for assessing volatility in the Forex market. Although the technology behind it is mathematically intricate, the takeaway for traders and investors is quite simple: Standard deviation indicates the probability that a given price value will fall within a certain range of the mean or average price over a given period of time.

## The Importance of Measuring Volatility in Forex

In any asset class, including Forex, volatility is an important concept. Volatility measures the day-to-day price movement of an asset, and investors use it to gauge market sentiment. High volatility suggests investor optimism, while low volatility suggests investor pessimism.

The concept of volatility is especially important in Forex. By nature, currencies tend to experience greater swings in value than other asset classes, which makes it more difficult to accurately predict future price movements. Traders and investors use a number of tools to assess and quantify volatility, including the standard deviation indicator.

## The Formula for Standard Deviation

The formula for standard deviation is fairly simple. For a given series of values, the calculation is as follows:

Standard Deviation = Square Root √([(Sum i)2 – (n*[Mean]2)/n-1])

Where,

Sum i = Ʃ (Xi – X Mean)2

Xi = the individual observation in the series
X Mean = the Mean or average observation
n = the number of observations

For a more detailed explanation of the formula, check out the Investopedia Standard Deviation tutorial.

## Applying Standard Deviation in Forex Trading Strategies

By taking a mathematical approach to the markets, traders and investors can better assess the probability of an asset’s future price movements. Standard deviation is an invaluable tool in this regard.

When applied to high and medium volatility instruments (e.g. EUR/USD pair), traders can use the standard deviation indicator to assess the probability of a given event occurring. For example, if the standard deviation is 5% over the past two weeks, the trader can assume that the EUR/USD has a 95% chance of trading within the range of 5% from the mean price at any given point within the next two weeks.

The standard Deviation indicator is also useful for trend strategies. By having a better understanding of the range of values within which the price is likely to remain, traders can better determine when a price has gone too far off course. High standard deviation readings suggest that the market may soon reverse as the price “reverts to the mean”. Low standard deviation readings indicate that the market may remain in a trading range, allowing traders to ride the wave without getting burned.

## Conclusion

In conclusion, the standard deviation indicator is a valuable tool for traders and investors when assessing volatility and predicting price movements. By applying a mathematical approach to the markets, traders and investors can gain a better understanding of the probability of a given event occurring. Furthermore, by having a greater clarity on the range of values within which the price is likely to remain, traders can better determine when a price has gone too far off course.

## Introduction to the Formula for Standard Deviation

Standard deviation is a powerful statistical tool used to measure the dispersion of data set points relative to their average value, or mean. It quantifies how spread out values are from one another and helps to identify the range of common and uncommon data points. To calculate the standard deviation of a data set, we’ll need to know the formula for standard deviation, its associated terms, and its application in real-world scenarios.

## What are the Terms of the Standard Deviation Formula?

Standard deviation is calculated using a number of simple terms. These include:

• the sum of all values in the data set (X);
• the number of values in the data set (N);
• the mean, or average, of the data set (μ); and
• the variance, the sum of squares of the difference between each data point and the mean of the data set.

## The Formula for Standard Deviation

The formula for standard deviation looks like this:

SD = √(( ∑ (X – μ)² ) / (N – 1) )

In this equation, X is the sum of values in the data set, μ is the mean of the data set, N is the number of values in the data set, and ( )² is the squares of the numbers inside the parentheses. To calculate the standard deviation of a data set, we’ll need to plug those terms into the formula and solve for SD.

## An Example of Applying the Formula for Standard Deviation

Let’s say we have a data set with values of 3, 7, 9, 13, and 15. To calculate the standard deviation of this data set, we’ll need to determine the values of X, N, and μ.

In this data set, X = 3 + 7 + 9 + 13 + 15 = 47, N = 5, and μ = 47/5 = 9.4. We can now plug these values into the standard deviation formula:

SD = √(( ∑ (X – μ)² ) / (N – 1) ) = √(( (3-9.4)² + (7-9.4)² + (9-9.4)² + (13-9.4)² + (15-9.4)² ) / (5 – 1) ) = √(236.8/4) = 7.26.

The standard deviation of our data set is 7.26. This means that, on average, our values are 7.26 numbers away from the mean of 9.4.