Loading the player...

What is the 'Arithmetic Mean'

The arithmetic mean is a mathematical representation of the typical value of a series of numbers, computed as the sum of all the numbers in the series divided by the count of all numbers in the series. The arithmetic mean is sometimes referred to as the average or simply as the mean. Some mathematicians and scientists prefer to use the term "arithmetic mean" to distinguish it from other measures of averaging, such as the geometric mean and the harmonic mean.

BREAKING DOWN 'Arithmetic Mean'

Nearly every field in mathematics and science uses the arithmetic mean. Many of the most common metrics in economics, such as per capita income and per capita gross domestic product (GDP), are calculated using arithmetic mean.

Suppose you wanted to know what the arithmetic mean of a stock's closing price was over the past week. If the stock closed at $14.50, $14.80, $15.20, $15.50 and then $14, its arithmetic mean closing price would be equal to the sum of the five numbers, $74, divided by 5, or $14.80.

Benefits of Arithmetic Mean

Perhaps the biggest benefit of using the arithmetic mean as a statistical measure is its simplicity. Anyone capable of simple addition followed by division can calculate the arithmetic mean of a data set. Of all the measures of central tendency, the arithmetic mean is least affected by fluctuations when multiple data sets are extracted from a larger population.

Limitations of Arithmetic Mean

In data sets that are skewed or where outliers are present, calculating the arithmetic mean often provides a misleading result. Consider a situation where 10 people are sitting at a restaurant table. Nine of them are teachers earning annual incomes of $45,000, while the 10th is a Silicon Valley entrepreneur who hit it big and earns $5 million per year. The arithmetic mean of their annual incomes is $540,500. This figure, however, in no way represents what the typical person at the table earns.

For data sets that do not follow a normal distribution pattern as represented by the bell curve, it is helpful to compare the arithmetic mean with other statistical measures, such as the median. In the above example, the median income at the table – the income at which half the people studied are above it and half are below it – is $45,000. This figure better represents the group as a whole than the arithmetic mean does. When the median and mean are far apart, as they are in this example, it indicates the data is skewed in the direction of the mean.

RELATED TERMS
  1. Mean

    The simple mathematical average of a set of two or more numbers. ...
  2. Arithmetic Index

    An index of securities that uses an arithmetic sum to determine ...
  3. Unweighted Index

    A simple arithmetic or geometric average used to calculate stock ...
  4. Harmonic Average

    The mean of a set of positive variables. Calculated by dividing ...
  5. Trimmed Mean

    A method of averaging that removes a small percentage of the ...
  6. Geometric Mean

    The average of a set of products, the calculation of which is ...
Related Articles
  1. Investing

    Calculating the Arithmetic Mean

    The arithmetic mean is the average of a sum of numbers.
  2. Investing

    Breaking Down The Geometric Mean

    Understanding portfolio performance, whether for a self-managed, discretionary portfolio or a non-discretionary portfolio, is vital to determining whether the portfolio strategy is working or ...
  3. Investing

    The Most Accurate Way To Gauge Returns: The Compound Annual Growth Rate

    The compound annual growth rate, or CAGR for short, represents one of the most accurate ways to calculate and determine returns for individual assets, investment portfolios and anything that ...
  4. Investing

    Explaining the Geometric Mean

    The average of a set of products, the calculation of which is commonly used to determine the performance results of an investment or portfolio.
  5. Investing

    4 Cases to Buy If the Stock Market Is at an All-Time High

    Learn about why someone would invest in the stock market, even if it has reached an all-time high. This article will review four cases for doing just that.
  6. Trading

    Trading With Gaussian Models Of Statistics

    The entire study of statistics originated from Gauss and allowed us to understand markets, prices and probabilities, among other applications.
  7. Investing

    How To Calculate Your Investment Return

    How much are your investments actually returning? Find out why the method of calculation matters.
  8. Investing

    Calculating Annualized Total Return

    The annualized total return is the average return of an investment each year over a given time period.
  9. Insights

    Explaining Income Per Capita

    Income per capita measures the amount of money that’s earned per person in a defined area.
  10. Investing

    The Uses And Limits Of Volatility

    Check out how the assumptions of theoretical risk models compare to actual market performance.
RELATED FAQS
  1. Can two numbers have the same arithmetic and geometric means?

    Learn about the often complicated relationship between the geometric mean and arithmetic mean for a set of numbers, and which ... Read Answer >>
  2. What is the difference between arithmetic and geometric averages?

    An arithmetic average is the sum of a series of numbers divided by the count of that series of numbers. If you were asked ... Read Answer >>
  3. The ABC Global mutual fund exhibited the following rates of return over the last ...

    The correct answer is: a) Arithmetic Mean = (15 + -7 + 6.5 + -11.3 + 32.7)/5 = 7.18% Geometric Mean =[(1.15 x 0.93 x 1.065 ... Read Answer >>
  4. How can investors benefit by understanding geometric means?

    Discover why investors should know the difference between geometric and arithmetic means, and why the geometric mean is more ... Read Answer >>
  5. How do you calculate the geometric mean to assess portfolio performance?

    Learn how to calculate the geometric mean. Understand when the geometric mean should be used and how it differs from the ... Read Answer >>
Hot Definitions
  1. Magna Cum Laude

    An academic level of distinction used by educational institutions to signify an academic degree which was received "with ...
  2. Cover Letter

    A written document submitted with a job application explaining the applicant's credentials and interest in the open position. ...
  3. 403(b) Plan

    A retirement plan for certain employees of public schools, tax-exempt organizations and certain ministers. Generally, retirement ...
  4. Master Of Business Administration - MBA

    A graduate degree achieved at a university or college that provides theoretical and practical training to help graduates ...
  5. Liquidity Event

    An event that allows initial investors in a company to cash out some or all of their ownership shares and is considered an ...
  6. Job Market

    A market in which employers search for employees and employees search for jobs. The job market is not a physical place as ...
Trading Center