This article is about the mathematical concept. For example, the population mean height is equal to the sum of the heights of every individual divided by the total number of individuals. The sample mean may differ from the population mean, probability and statistics schaum’s outline series pdf for small samples.

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Equality holds if and only if all the elements of the given sample are equal. Geometric visualisation of the mode, median and mean of an arbitrary probability density function. For example, mean income is typically skewed upwards by a small number of people with very large incomes, so that the majority have an income lower than the mean. By contrast, the median income is the level at which half the population is below and half is above. The mode income is the most likely income, and favors the larger number of people with lower incomes. Hölder mean, is an abstraction of the quadratic, arithmetic, geometric and harmonic means.

In other applications they represent a measure for the reliability of the influence upon the mean by the respective values. Sometimes a set of numbers might contain outliers, i. It involves discarding given parts of the data at the top or the bottom end, typically an equal amount at each end, and then taking the arithmetic mean of the remaining data. The number of values removed is indicated as a percentage of total number of values. It is simply the arithmetic mean after removing the lowest and the highest quarter of values.