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Arithmetic Mean Definition

Arithmetic Mean, or simply the mean or average is the central tendency of a collection of numbers taken as the sum of the numbers divided by the size of the collection and the collection is often the sample space. The term "arithmetic mean" is preferred in mathematics and statistics because it helps distinguish it from other averages such as the geometric mean as well as the harmonic mean.

The average often used to describe central tendency as it is not a robust statistic meaning that it is greatly influenced by outliers and the arithmetic mean may not accord with one's notion of "middle" and robust statistics such as the median may be a better description of central tendency.

Arithmetic Mean Assignment Help

Suppose the sample space is and then the mean is defined via the equation and it is expressed as follows:

If the list is a statistical population then the mean of that population is called a population mean and if the list is a sampling, then the resulting statistic is known as the sample mean. The mean of a variable is often denoted by a bar and the arithmetic mean has several properties that make it useful which is used as a measure of central tendency. If the numbers have mean X, then, then is the distance from a given number to the mean.

If it is required to use a single number X as an estimate for the value of numbers, then the average does this in the sense of minimizing the sum of squares (xi − X)2 of the errors and residuals in statistics and it follows that the mean is also the best single predictor in the sense of having the lowest root mean squared error. For a distribution that is normal, the average or means is equal to both the median and the mode as well as other measures of central tendency.

Arithmetic Mean Homework Help

The mean may be mistakenly interpreted as the median to imply that most values are higher or lower than it is actually the case and if elements in the sample space are in the arithmetic progression then it is placed in some order and then the median, as well as the arithmetic average, are equal.

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