A:

While there are many different ways to measure variability within a set of data, two of the most popular are standard deviation and average deviation. Though very similar, the calculation and interpretation of these two differ in some key ways. Determining range and volatility is especially important in the finance industry, so professionals in areas such as accounting, investing and economics should be very familiar with both concepts.

Standard deviation is the most common measure of variability and is frequently used to determine the volatility of stock markets or other investments. To calculate the standard deviation, you must first determine the variance. This is done by subtracting the mean from each data point and then squaring, summing and averaging the differences. Variance in itself is an excellent measure of variability and range, as a larger variance reflects a greater spread in the underlying data. The standard deviation is simply the square root of the variance. Squaring the differences between each point and the mean avoids the issue of negative differences for values below the mean, but it means the variance is no longer in the same unit of measure as the original data. Taking the root of the variance means the standard deviation returns to the original unit of measure and is easier to interpret and utilize in further calculations.

The average deviation, also called the mean absolute deviation, is another measure of variability. However, average deviation utilizes absolute values instead of squares to circumvent the issue of negative differences between data and the mean. To calculate the average deviation, simply subtract the mean from each value, then sum and average the absolute values of the differences. The mean absolute value is used less frequently because the use of absolute values makes further calculations more complicated and unwieldy than using the simple standard deviation.

RELATED FAQS
  1. The Difference Between the Expected Return and the Standard Deviation of a Portfolio

    Expected return and standard deviation are two statistical measures that can be used to analyze a portfolio. Read Answer >>
  2. How can you calculate volatility in Excel?

    Historical volatility is a long-term assessment of risk. Here's how to calculate it in Excel. Read Answer >>
  3. Relative Standard Error

    Distinguish between mean, standard deviation, standard error and relative standard error in statistical survey samples. Read Answer >>
  4. What Is the Formula for Calculating Beta?

    Learn about beta, how to calculate it, and how it's used as a risk measure with examples that include Apple and Tesla. Read Answer >>
  5. What is the downside of investing in the utility sector?

    Learn about the pros and cons of investing in the utility sector, and determine whether the steady dividend income possibility ... Read Answer >>
Related Articles
  1. Trading

    Trading with Gaussian models of statistics

    The study of statistics originated from Carl Friedrich Gauss and helps us understand markets, prices and probabilities, among other applications.
  2. Investing

    Understanding The Sharpe Ratio

    The Sharpe ratio describes how much excess return you are receiving for the extra volatility that you endure for holding a riskier asset.
  3. Trading

    Improve your investing with Excel

    Find out how to use Excel, a useful tool for assisting with investment organizations and evaluations.
  4. Trading

    How To Convert Value At Risk To Different Time Periods

    Volatility is not the only way to measure risk. Learn about the "new science of risk management".
  5. Investing

    Using Historical Volatility To Gauge Future Risk

    Use these calculations to uncover the risk involved in your investments.
  6. Investing

    Understanding Volatility Measurements

    Learn how to choose a fund with an optimal risk-reward combination. Find more information about standard deviation, beta, and more.
  7. Investing

    5 ways to measure mutual fund risk

    Statistical measures such as alpha and beta can help investors understand investment risk on mutual funds and how it relates to returns.
  8. Investing

    Computing Historical Volatility in Excel

    We examine how annualized historical volatility is computed from daily log returns, variance and standard deviation.
RELATED TERMS
  1. Standard Deviation

    The standard deviation is a statistic that measures the dispersion ...
  2. Variability

    Variability is the extent to which data points in a statistical ...
  3. Downside Risk

    Downside risk is an estimate of a security's potential to suffer ...
  4. Downside Deviation

    Downside deviation is a measure of downside risk that focuses ...
  5. Sum Of Squares

    Sum of Squares is a statistical technique used in regression ...
  6. Mean-Variance Analysis

    Mean-variance analysis is the process of weighing risk against ...
Trading Center