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The mode of a sample is the element that occurs most often in the collection. For example, the mode of the sample [1, 3, 6, 6, 6, 6, 7, 7, 12, 12, 17] is 6. Given the list of data [1, 1, 2, 4, 4] its mode is not unique. A dataset, in such a case, is said to be bimodal, while a set with more than two modes may be described as multimodal.
For example, given binary data, say heads or tails, if a data set consists of 2 heads and 1 tails, then the mode is "heads", but the empirical measure is 2/3 heads, 1/3 tails, which minimizes the cross-entropy (total surprisal) from the data set.
The mode income is the most likely income and favors the larger number of people with lower incomes. While the median and mode are often more intuitive measures for such skewed data, many skewed distributions are in fact best described by their mean, including the exponential and Poisson distributions.
The term "mode" in this context refers to any peak of the distribution, not just to the strict definition of mode which is usual in statistics. If there is a single mode, the distribution function is called "unimodal". If it has more modes it is "bimodal" (2), "trimodal" (3), etc., or in general, "multimodal". [2]
Examples are the simple gravitation law connecting masses and distance with the resulting force, or the formula for equilibrium concentrations of chemicals in a solution that connects concentrations of educts and products. Assuming log-normal distributions of the variables involved leads to consistent models in these cases.
'Mean, median, mode and skewness', A tutorial devised for first-year psychology students at Oxford University, based on a worked example. The Complex SAT Math Problem Even the College Board Got Wrong: Andrew Daniels in Popular Mechanics
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Average of chords. In ordinary language, an average is a single number or value that best represents a set of data. The type of average taken as most typically representative of a list of numbers is the arithmetic mean – the sum of the numbers divided by how many numbers are in the list.