Overhead bar in the context of Mathematical notation


Overhead bar in the context of Mathematical notation

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⭐ Core Definition: Overhead bar

An overline, overscore, or overbar, is a typographical feature of a horizontal line drawn immediately above the text. In old mathematical notation, an overline was called a vinculum, a notation for grouping symbols which is expressed in modern notation by parentheses, though it persists for symbols under a radical sign. The original use in Ancient Greek was to indicate compositions of Greek letters as Greek numerals. In Latin, it indicates Roman numerals multiplied by a thousand and it forms medieval abbreviations (sigla). Marking one or more words with a continuous line above the characters is sometimes called overstriking, though overstriking generally refers to printing one character on top of an already-printed character.

An overline, that is, a single line above a chunk of text, should not be confused with the macron, a diacritical mark placed above (or sometimes below) individual letters. The macron is narrower than the character box.

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Overhead bar in the context of Mean

A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statistics. Each attempts to summarize or typify a given group of data, illustrating the magnitude and sign of the data set. Which of these measures is most illuminating depends on what is being measured, and on context and purpose.

The arithmetic mean, also known as "arithmetic average", is the sum of the values divided by the number of values. The arithmetic mean of a set of numbers x1, x2, ..., xn is typically denoted using an overhead bar, . If the numbers are from observing a sample of a larger group, the arithmetic mean is termed the sample mean () to distinguish it from the group mean (or expected value) of the underlying distribution, denoted or .

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