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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. While the arithmetic mean is often used to report central tendencies , it is not a robust statistic , meaning that it is greatly influenced by outliers values that are very much larger or smaller than most of the values.

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. While the arithmetic mean is often used to report central tendencies , it is not a robust statistic , meaning that it is greatly influenced by outliers values that are very much larger or smaller than most of the values. For skewed distributions , such as the distribution of income for which a few people's incomes are substantially greater than most people's, the arithmetic mean may not coincide with one's notion of "middle", and robust statistics, such as the median , may provide better description of central tendency.

The arithmetic mean is the most commonly used and readily understood measure of central tendency in a data set. In statistics, the term average refers to any of the measures of central tendency. The arithmetic mean of a set of observed data is defined as being equal to the sum of the numerical values of each and every observation, divided by the total number of observations. For example, consider the monthly salary of 10 employees of a firm: , , , , , , , , , The arithmetic mean is.

If the data set is a statistical population i. The arithmetic mean can be similarly defined for vectors in multiple dimension, not only scalar values; this is often referred to as a centroid.

More generally, because the arithmetic mean is a convex combination coefficients sum to 1 , it can be defined on a convex space , not only a vector space. The arithmetic mean has several properties that make it useful, especially as a measure of central tendency. These include:. The arithmetic mean may be contrasted with the median.

The median is defined such that no more than half the values are larger than, and no more than half are smaller than, the median. If elements in the data increase arithmetically , when placed in some order, then the median and arithmetic average are equal.

The average is 2. In this case, the arithmetic average is 6. In general, the average value can vary significantly from most values in the sample, and can be larger or smaller than most of them. There are applications of this phenomenon in many fields. For example, since the s, the median income in the United States has increased more slowly than the arithmetic average of income. A weighted average, or weighted mean, is an average in which some data points count more heavily than others, in that they are given more weight in the calculation.

If a numerical property, and any sample of data from it, could take on any value from a continuous range, instead of, for example, just integers, then the probability of a number falling into some range of possible values can be described by integrating a continuous probability distribution across this range, even when the naive probability for a sample number taking one certain value from infinitely many is zero.

The analog of a weighted average in this context, in which there are an infinite number of possibilities for the precise value of the variable in each range, is called the mean of the probability distribution. This equality does not hold for other probability distributions, as illustrated for the lognormal distribution here.

Particular care must be taken when using cyclic data, such as phases or angles. This is incorrect for two reasons:. In general application, such an oversight will lead to the average value artificially moving towards the middle of the numerical range. A solution to this problem is to use the optimization formulation viz. From Wikipedia, the free encyclopedia. Numbers average. For broader coverage of this topic, see Mean. Main article: Median. Main article: Weighted average.

Main article: Mean of circular quantities. Math Vault. Retrieved 21 August Statistical Methods: An Introductory Text. New Age International. The American Prospect.

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Correlation Regression analysis Correlation Pearson product-moment Partial correlation Confounding variable Coefficient of determination. GND : Simply put: AnalystNotes offers the best value and the best product available to help you pass your exams. Quantitative Methods 1 Reading 7. Statistical Concepts and Market Returns Subject 4. Measures of Center Tendency. Why should I choose AnalystNotes?

Mean is typically the best measure of central tendency because it takes all values into account. Note that Mean can only be defined on interval and ratio level of measurement. Median is the mid point of data when it is arranged in order. It is typically when the data set has extreme values or is skewed in some direction. Note that median is defined on ordinal, interval and ratio level of measurement.

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. Advantages and disadvantages of Geometric Mean · It is rigidly defined. · It is based upon all the observations. · It is suitable for further.

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.

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