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The term "arithmetic mean" is preferred in some contexts in mathematics and statistics, because it helps distinguish it from other means , such as the geometric mean and the harmonic mean. In addition to mathematics and statistics, the arithmetic mean is used frequently in many diverse fields such as economics , anthropology and history , and it is used in almost every academic field to some extent. For example, per capita income is the arithmetic average income of a nation's population.

## Harmonic Mean (H.M), its Merits, Demerits and Uses

It can be easily calculated; and can be easily understood. It is the reason that it is the most used measure of central tendency. Fluctuations are minimum for this measure of central tendency when repeated samples are taken from one and the same population. It can further be subjected to algebraic treatment unlike other measures i. A single item can bring big change in the result. For example if there are three terms 4, 7, 10 ; X is 7 in this case.

Its value will be effective only if the frequency is normally distributed. Otherwise in case skewness is more, the results become ineffective. In case of open end class intervals we have to assume the limits of such intervals and a little variation in X can take place. Such is not the case with median and mode, and there is no use of the open end intervals in its calculations.

Qualitative forms such as Cleverness, Riches etc. Sometimes it gives impossible or laughable conclusions, e. Article Shared by Pooja Mehta. Related Articles. How to Calculate Weighted Arithmetic Mean? ## Merits and Demerits of Arithmetic Mean

In any research, enormous data is collected and, to describe it meaningfully, one needs to summarise the same. The bulkiness of the data can be reduced by organising it into a frequency table or histogram. These measures may also help in the comparison of data. The mean, median and mode are the three commonly used measures of central tendency. Mean is the most commonly used measure of central tendency. There are different types of mean, viz. If mentioned without an adjective as mean , it generally refers to the arithmetic mean.

Before you order, simply sign up for a free user account and in seconds you'll be experiencing the best in CFA exam preparation. Quantitative Methods 1 Reading 7. Statistical Concepts and Market Returns Subject 4. Measures of Center Tendency. Seeing is believing! Find out more. Subject 4. ## Geometric mean

In mathematics , the harmonic mean is one of several kinds of average , and in particular, one of the Pythagorean means. Typically, it is appropriate for situations when the average of rates is desired. The harmonic mean can be expressed as the reciprocal of the arithmetic mean of the reciprocals of the given set of observations. As a simple example, the harmonic mean of 1, 4, and 4 is. The third formula in the above equation expresses the harmonic mean as the reciprocal of the arithmetic mean of the reciprocals.

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Arithmetic average, or arithmetic mean , or just mean , is probably the simplest tool in statistics, designed to measure central tendency in a data set which can be a group of stocks or returns of a stock in particular years. Using arithmetic average has advantages and disadvantages, and in some cases you may find other measures like geometric average or median more suitable. On this page:. As the most basic measure in statistics, arithmetic average is very easy to calculate. For a small data set, you can calculate the arithmetic mean quickly in your head or on a piece of paper. It can be easily calculated; and can be easily understood. It is the reason that it is the most used measure of central tendency.

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