The arithmetic mean is the average of a set of positive real numbers, but can be influenced by outliers. It is commonly used in many fields, but the geometric and harmonic means may provide more accurate information in certain situations.
The arithmetic mean is a measure of central tendency calculated by adding the values of all numbers within a set and dividing the total by the amount of items in the set. All numbers in the set must be positive real numbers. The terms mean and mean also refer to the arithmetic mean and are more commonly used in real-life situations.
As distinct from geometric mean and harmonic mean values, the arithmetic mean is always greater than or equal to the geometric mean. The geometric mean is always greater than or equal to the harmonic mean, when only positive real numbers are used. Together, the arithmetic mean, geometric mean, and harmonic mean are referred to as the three Pythagorean means.
When the lowest and highest number in a set are compared to the arithmetic mean of a set, the mean will always lie between the lowest and highest number. However, the mean is not always in the middle of the set of numbers. This is because it can be strongly influenced by the presence of extremely high or extremely low values, also called outliers. For this reason, there are other measures of central tendency, such as mean and fashion, to help describe a whole.
An example is a set whose values are 4, 6, 7, 10, 13, and 34. The mean is equal to 12.3, which is more than one person’s sense of where the center might be. However, when one value, 34, is changed to 14 to more closely match the others, the arithmetic mean is 9. Despite its weaknesses, the arithmetic mean is commonly used in most academic fields other than statistics and mathematics, in especially economics, social sciences, and history.
When it comes to the arithmetic mean, half of the values must be above the mean of a set, while the other half of the values must be below the mean. This does not apply to the number of items in the set. The arithmetic mean serves as the fulcrum of a balance for the values.
While the arithmetic mean is a commonly understood concept and easy to calculate, there are situations where the geometric or harmonic mean provides more accurate information about a set of values. Frequently, the harmonic mean has applications for engineering data, especially when determining means of speeds. The geometric mean can be descriptive of economic data, proportional growth, or social science statistics.
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