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.
62-653: 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. In most forms of Latin scribal abbreviation , an overline or macron indicates omitted letters similar to use of apostrophes in English contractions. Letters with macrons or overlines continue to be used in medical abbreviations in various European languages, particularly for prescriptions . Common examples include Note, however, that abbreviations involving
124-445: A + b i ; z ¯ = a − b i {\displaystyle z=a+bi;\quad {\overline {z}}=a-bi} and to represent a line segment in geometry (e.g., A B ¯ {\displaystyle {\overline {AB}}} ), sample means in statistics (e.g., X ¯ {\displaystyle {\overline {X}}} ) and negations in logic . It
186-905: A repeating decimal value: 1 7 = 0. 142857 ¯ = 0.142857142857142857142857... {\displaystyle {1 \over 7}=0.{\overline {142857}}=0.142857142857142857142857...} When it is not possible to format the number so that the overline is over the digit(s) that repeat, one overline character is placed to the left of the digit(s) that repeat: 3. I ¯ 3 = 3. 3 ¯ = 3.3333333333333333333333333... {\displaystyle 3.{\overline {\phantom {I}}}3=3.{\overline {3}}=3.3333333333333333333333333...} 3.12 I ¯ 34 = 3.12 34 ¯ = 3.123434343434343434343434... {\displaystyle 3.12{\overline {\phantom {I}}}34=3.12{\overline {34}}=3.123434343434343434343434...} Historically,
248-504: A ] or a . In topology , the closure of a subset S of a topological space is often denoted S or cl S {\displaystyle \operatorname {cl} S} . In crystallography , an overline indicates an improper rotation or a negative number : In computational neuroscience , an overline is used to indicate the "maximal" conductances in Hodgkin-Huxley models . This goes back to at least
310-429: A diacritic will be written like a macron, although it represents another diacritic whose standard form is different: Continuing previous Latin scribal abbreviations , letters with combining macron can be used in various European languages to represent the overlines indicating various medical abbreviations , particularly including: Note, however, that abbreviations involving the letter h take their macron halfway up
372-643: A double-bar (or double-prime) to represent phrasal-level units. X-bar theory derives its name from the overbar. One of the core proposals of the theory was the creation of an intermediate syntactic node between phrasal (XP) and unit (X) levels; rather than introduce a different label, the intermediate unit was marked with a bar. In HTML using CSS , overline is implemented via the text-decoration property; for example, <span style="text-decoration: overline">text</span> results in: text . The text decoration property supports also other typographical features with horizontal lines: underline (a line below
434-649: A menu option to edit Overlining in Microsoft Word for any operating system, or in Word for the web. Overlining can be added using fields codes, EQ \O() . The field code {EQ \O(x,¯)} produces x and the field code {EQ \O(xyz,¯¯¯)} produces xyz ; However this does not work in Word on Android, ChromeOS, iPadOS, or Word for the web. In Word 2010 it is necessary to insert an MS Equation object. Overstriking of longer sections of text, such as in 123 , can also be produced in many text processors as text markup as
496-551: A number of vernacular languages of the Solomon Islands and Vanuatu , particularly those first transcribed by Anglican missionaries . The macron has no unique value, and is simply used to distinguish between two different phonemes. Thus, in several languages of the Banks Islands , including Mwotlap , the simple m stands for /m/ , but an m with a macron ( m̄ ) is a rounded labial-velar nasal /ŋ͡mʷ/ ; while
558-406: A reversal of its official name (and compatibility decomposition), it is much wider than an actual macron diacritic over most letters, and actually wider than U+203E ‾ OVERLINE in most fonts. In ChromeOS and Linux , the symbol can be added using the keystrokes Ctrl + ⇧ Shift + U to activate Unicode input , then type "00AF" as the code for the character. On a Mac , with
620-418: A row vector whose j element ( j = 1, ..., K ) is one of the random variables. The sample covariance matrix has N − 1 {\displaystyle \textstyle N-1} in the denominator rather than N {\displaystyle \textstyle N} due to a variant of Bessel's correction : In short, the sample covariance relies on the difference between each observation and
682-401: A sample of Fortune 500 companies. In this case, there is not just a sample variance for each variable but a sample variance-covariance matrix (or simply covariance matrix ) showing also the relationship between each pair of variables. This would be a 3×3 matrix when 3 variables are being considered. The sample covariance is useful in judging the reliability of the sample means as estimators and
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#1732786910130744-495: A sample, which is the sum of those values divided by the number of values. Using mathematical notation, if a sample of N observations on variable X is taken from the population, the sample mean is: Under this definition, if the sample (1, 4, 1) is taken from the population (1,1,3,4,0,2,1,0), then the sample mean is x ¯ = ( 1 + 4 + 1 ) / 3 = 2 {\displaystyle {\bar {x}}=(1+4+1)/3=2} , as compared to
806-586: A special form of understriking. Collabora Online , Collabora Office and LibreOffice have direct menu support for several styles of Overline in the "Format" menu within applications of their office suites, including spreadsheets, presentations and graphics applications. The user-interface option is available in the web based suite, and the locally installable applications for Linux, macOS and Windows, and with Collabora Office in Android (in tablet format), ChromeOS and iPadOS. Options for Overline are available under
868-550: Is a diacritical mark : it is a straight bar ¯ placed above a letter, usually a vowel . Its name derives from Ancient Greek μακρόν ( makrón ) 'long' because it was originally used to mark long or heavy syllables in Greco-Roman metrics . It now more often marks a long vowel . In the International Phonetic Alphabet , the macron is used to indicate a mid-tone ; the sign for a long vowel
930-444: Is a random variable , not a constant, since its calculated value will randomly differ depending on which members of the population are sampled, and consequently it will have its own distribution. For a random sample of n independent observations, the expected value of the sample mean is and the variance of the sample mean is If the samples are not independent, but correlated , then special care has to be taken in order to avoid
992-587: Is a column vector whose j -th element x ¯ j {\displaystyle {\bar {x}}_{j}} is the average value of the N observations of the j variable: Thus, the sample mean vector contains the average of the observations for each variable, and is written The sample covariance matrix is a K -by- K matrix Q = [ q j k ] {\displaystyle \textstyle \mathbf {Q} =\left[q_{jk}\right]} with entries where q j k {\displaystyle q_{jk}}
1054-435: Is a macron, there are no other diacritics used above letters, so in practice other diacritics can and have been used in less polished writing or print, yielding nonstandard letters like ã ñ õ û , depending on displayability of letters in computer fonts . In Obolo , the simple n stands for the common alveolar nasal /n/ , while an n with macron ( n̄ ) represents the velar nasal /ŋ/ . Also, in some instances,
1116-569: Is also used in Hermann–Mauguin notation . In music, the tenuto marking resembles the macron. The macron is also used in German lute tablature to distinguish repeating alphabetic characters. The Unicode Standard encodes combining and precomposed macron characters: Macron-related Unicode characters not included in the table above: In TeX a macron is created with the command "\=", for example: M\=aori for Māori. In OpenOffice , if
1178-410: Is also useful as an estimate of the population covariance matrix. Due to their ease of calculation and other desirable characteristics, the sample mean and sample covariance are widely used in statistics to represent the location and dispersion of the distribution of values in the sample, and to estimate the values for the population. The sample mean is the average of the values of a variable in
1240-455: Is an N by 1 vector of ones. If the observations are arranged as rows instead of columns, so x ¯ {\displaystyle \mathbf {\bar {x}} } is now a 1× K row vector and M = F T {\displaystyle \mathbf {M} =\mathbf {F} ^{\mathrm {T} }} is an N × K matrix whose column j is the vector of N observations on variable j , then applying transposes in
1302-451: Is an estimate of the covariance between the j variable and the k variable of the population underlying the data. In terms of the observation vectors, the sample covariance is Alternatively, arranging the observation vectors as the columns of a matrix, so that which is a matrix of K rows and N columns. Here, the sample covariance matrix can be computed as where 1 N {\displaystyle \mathbf {1} _{N}}
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#17327869101301364-435: Is calculated using the variance of the sample. If the sample is random, the standard error falls with the size of the sample and the sample mean's distribution approaches the normal distribution as the sample size increases. The term "sample mean" can also be used to refer to a vector of average values when the statistician is looking at the values of several variables in the sample, e.g. the sales, profits, and employees of
1426-533: Is designated by an overline, e.g. RESET , representing logical negation . Overlining is also used in graphics design for decoration of text to help convey a message. Some Morse code prosigns can be expressed as two or three characters run together, and an overline is often used to signify this. The most famous is the distress signal , SOS . An overline-like symbol is traditionally used in Syriac text to mark abbreviations and numbers. It has dots at each end and
1488-581: Is given by and the elements q j k {\displaystyle q_{jk}} of the weighted covariance matrix Q {\displaystyle \textstyle \mathbf {Q} } are If all weights are the same, w i = 1 / N {\displaystyle \textstyle w_{i}=1/N} , the weighted mean and covariance reduce to the (biased) sample mean and covariance mentioned above. The sample mean and sample covariance are not robust statistics , meaning that they are sensitive to outliers . As robustness
1550-487: Is instead a modified triangular colon ⟨ ː ⟩. The opposite is the breve ⟨˘⟩ , which marks a short or light syllable or a short vowel. In Greco-Roman metrics and in the description of the metrics of other literatures, the macron was introduced and is still widely used in dictionaries and educational materials to mark a long (heavy) syllable . Even relatively recent classical Greek and Latin dictionaries are still concerned with indicating only
1612-430: Is positive definite if and only if the rank of the x i . − x ¯ {\displaystyle \mathbf {x} _{i}.-\mathbf {\bar {x}} } vectors is K. The sample mean and the sample covariance matrix are unbiased estimates of the mean and the covariance matrix of the random vector X {\displaystyle \textstyle \mathbf {X} } ,
1674-417: Is the voiced velar fricative /ɣ/ . In Marshallese , a macron is used on four letters – ā n̄ ō ū – whose pronunciations differ from the unmarked a n o u . Marshallese uses a vertical vowel system with three to four vowel phonemes, but traditionally their allophones have been written out, so vowel letters with macron are used for some of these allophones. Though the standard diacritic involved
1736-438: Is the population variance. The arithmetic mean of a population , or population mean, is often denoted μ . The sample mean x ¯ {\displaystyle {\bar {x}}} (the arithmetic mean of a sample of values drawn from the population) makes a good estimator of the population mean, as its expected value is equal to the population mean (that is, it is an unbiased estimator ). The sample mean
1798-576: Is used as a length mark in Odia script . Collabora Online , an office suite for the web has direct menu support for several styles of Overline in the "Format" menu, with options available under "Format > Character" enabling the default solid Overline to be replaced with double overline, dots, dashes, waves, double waves, and the color of the Overline can be set. Collabora Office and LibreOffice have direct menu support for several styles of Overline in
1860-547: The ABC Extended keyboard, use ⌥ Option + a . In Microsoft Windows , U+00AF can be entered with the keystrokes Alt + 0 1 7 5 (where numbers are entered from the numeric keypad ). The Unicode character U+070F SYRIAC ABBREVIATION MARK is used to mark Syriac abbreviations and numbers . However, several computer environments do not render this line correctly or at all. The Unicode character U+0B55 ୕ ORIYA SIGN OVERLINE
1922-478: The Fortune 500 might be used for convenience instead of looking at the population, all 500 companies' sales. The sample mean is used as an estimator for the population mean, the average value in the entire population, where the estimate is more likely to be close to the population mean if the sample is large and representative. The reliability of the sample mean is estimated using the standard error , which in turn
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1984-401: The K random variables) is assigned a weight w i ≥ 0 {\displaystyle \textstyle w_{i}\geq 0} . Without loss of generality, assume that the weights are normalized : (If they are not, divide the weights by their sum). Then the weighted mean vector x ¯ {\displaystyle \textstyle \mathbf {\bar {x}} }
2046-422: The alveolar trill /r/ – by contrast with r , which encodes the alveolar flap /ɾ/ . In Bislama (orthography before 1995), Lamenu and Lewo , a macron is used on two letters m̄ p̄ . m̄ represents /mʷ/ , and p̄ represents /pʷ/ . The orthography after 1995 (which has no diacritics) has these written as mw and pw . In Kokota , ḡ is used for the velar stop /ɡ/ , but g without macron
2108-431: The equivalence class of the integer a , denoted by a n , is the set {... , a − 2 n , a − n , a , a + n , a + 2 n , ... }. This set, consisting of all the integers congruent to a modulo n , is called the congruence class , residue class , or simply residue of the integer a modulo n . When the modulus n is known from the context, that residue may also be denoted [
2170-418: The j random variable ( j =1,..., K ). These observations can be arranged into N column vectors, each with K entries, with the K ×1 column vector giving the i -th observations of all variables being denoted x i {\displaystyle \mathbf {x} _{i}} ( i =1,..., N ). The sample mean vector x ¯ {\displaystyle \mathbf {\bar {x}} }
2232-411: The sample covariance or empirical covariance are statistics computed from a sample of data on one or more random variables . The sample mean is the average value (or mean value ) of a sample of numbers taken from a larger population of numbers, where "population" indicates not number of people but the entirety of relevant data, whether collected or not. A sample of 40 companies' sales from
2294-453: The "Format" menu. The user-interface option is available in their word processors on Linux, macOS and Windows, and also in Android (in tablet format), ChromeOS and iPadOS with Collabora Office. Options for Overline are available under the menu: "Format > Character", enabling the default solid Overline to be replaced with double overline, dots, dashes, waves, double waves, and the color of the Overline can be set. Microsoft Word does not have
2356-403: The appropriate places yields Like covariance matrices for random vector , sample covariance matrices are positive semi-definite . To prove it, note that for any matrix A {\displaystyle \mathbf {A} } the matrix A T A {\displaystyle \mathbf {A} ^{T}\mathbf {A} } is positive semi-definite. Furthermore, a covariance matrix
2418-478: The ascending line rather than at the normal height for unicode macrons and overlines: ħ . This is separately encoded in Unicode with the symbols using bar diacritics and appears shorter than other macrons in many fonts. The overline is a typographical symbol similar to the macron, used in a number of ways in mathematics and science. For example, it is used to represent complex conjugation : z =
2480-468: The center. In German it is occasionally used to indicate a pair of letters which cannot both be fitted into the available space. When Morse code is written out as text, overlines are used to distinguish prosigns and other concatenated character groups from strings of individual characters. In Arabic writing and printing , overlines are traditionally used instead of underlines for typographic emphasis , although underlines are used more and more due to
2542-489: The denominator. This is an example of why in probability and statistics it is essential to distinguish between random variables (upper case letters) and realizations of the random variables (lower case letters). The maximum likelihood estimate of the covariance for the Gaussian distribution case has N in the denominator as well. The ratio of 1/ N to 1/( N − 1) approaches 1 for large N , so
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2604-476: The extension Compose Special Characters is installed, a macron may be added by following the letter with a hyphen and pressing the user's predefined shortcut key for composing special characters. A macron may also be added by following the letter with the character's four-digit hex-code, and pressing the user's predefined shortcut key for adding unicode characters. Sample mean The sample mean ( sample average ) or empirical mean ( empirical average ), and
2666-506: The font. In Unicode, character U+FE26 COMBINING CONJOINING MACRON is conjoining (bridging) two characters: ◌︦◌ . In East Asian ( CJK ) computing, U+FFE3 ￣ FULLWIDTH MACRON is available. Despite the name, Unicode maps this character to both U+203E and U+00AF. Unicode maps the overline-like character from ISO/IEC 8859-1 and code page 850 to the U+00AF ¯ MACRON symbol mentioned above. In
2728-486: The integral part of a number from its fractional part , as in 9 9 95 (meaning 99.95 in decimal point format). A similar notation remains in common use as an underbar to superscript digits, especially for monetary values without a decimal separator, as in 99. In mathematics, an overline can be used as a vinculum . The vinculum can indicate a line segment : A B ¯ {\displaystyle {\overline {\rm {AB}}}} The vinculum can indicate
2790-436: The landmark paper published by Nobel prize winners Alan Lloyd Hodgkin and Andrew Fielding Huxley around 1952. Overlines are used in subatomic particle physics to denote antiparticles for some particles (with the alternate being distinguishing based on electric charge). For example, the proton is denoted as p , and its corresponding antiparticle is denoted as p . An active low signal
2852-402: The latter allows an overline to be placed over any character. There is also U+033F ◌̿ COMBINING DOUBLE OVERLINE . As with any combining character , it appears in the same character box as the character that logically precedes it: for example, x̅, compared to x‾. A series of overlined characters, for example 1̅2̅3̅, may result either in a broken or an unbroken line, depending on
2914-499: The length (weight) of syllables; that is why most still do not indicate the length of vowels in syllables that are otherwise metrically determined. Many textbooks about Ancient Rome and Greece use the macron, even if it was not actually used at that time (an apex was used if vowel length was marked in Latin). The following languages or transliteration systems use the macron to mark long vowels : The following languages or alphabets use
2976-469: The letter h take their macron halfway up the ascending line rather than at the normal height for Unicode overlines and macrons: ħ . This is separately encoded in Unicode with the symbols using bar diacritics and appears shorter than other overlines in many fonts. In the Middle Ages , from the original Indian decimal writing , before printing, an overline over the units digit was used to separate
3038-411: The macron to mark tones : Sometimes the macron marks an omitted n or m , like the tilde , in which context it is referred to as a " nasal suspension": In romanizations of Hebrew , the macron below is typically used to mark the begadkefat consonant lenition . However, for typographical reasons a regular macron is used on p and g instead: p̄, ḡ . The macron is used in the orthography of
3100-416: The mantissa remains positive. This notation avoids the need for separate tables to convert positive and negative logarithms back to their original numbers. The overline notation can indicate a complex conjugate and analogous operations. In physics, an overline sometimes indicates a vector , although boldface and arrows are also commonly used: Congruence modulo n is an equivalence relation , and
3162-467: The maximum likelihood estimate approximately equals the unbiased estimate when the sample is large. For each random variable, the sample mean is a good estimator of the population mean, where a "good" estimator is defined as being efficient and unbiased. Of course the estimator will likely not be the true value of the population mean since different samples drawn from the same distribution will give different sample means and hence different estimates of
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#17327869101303224-519: The menu: "Format > Character", enabling the default solid Overline to be replaced with double overline, dots, dashes, waves, double waves, and the color of the Overline can be set. In LaTeX , a text <text> can be overlined with $ \overline{\mbox{<text>}}$ . The inner \mbox{} is necessary to override the math-mode (here invoked by the dollar signs) which the \overline{} demands. Macron (diacritic) A macron ( / ˈ m æ k r ɒ n , ˈ m eɪ -/ MAK -ron, MAY - )
3286-399: The population mean of μ = ( 1 + 1 + 3 + 4 + 0 + 2 + 1 + 0 ) / 8 = 12 / 8 = 1.5 {\displaystyle \mu =(1+1+3+4+0+2+1+0)/8=12/8=1.5} . Even if a sample is random, it is rarely perfectly representative, and other samples would have other sample means even if the samples were all from
3348-539: The problem of pseudoreplication . If the population is normally distributed , then the sample mean is normally distributed as follows: If the population is not normally distributed, the sample mean is nonetheless approximately normally distributed if n is large and σ / n < +∞. This is a consequence of the central limit theorem . In a weighted sample, each vector x i {\displaystyle \textstyle {\textbf {x}}_{i}} (each set of single observations on each of
3410-499: The rise of the internet. X-bar theory makes use of overbar notation to indicate differing levels of syntactic structure . Certain structures are represented by adding an overbar to the unit, as in X . Due to difficulty in typesetting the overbar, the prime symbol is often used instead, as in X ′ . Contemporary typesetting software, such as LaTeX, has made typesetting overbars considerably simpler ; both prime and overbar markers are accepted usages. Some variants of X-bar notation use
3472-437: The same population. The sample (2, 1, 0), for example, would have a sample mean of 1. If the statistician is interested in K variables rather than one, each observation having a value for each of those K variables, the overall sample mean consists of K sample means for individual variables. Let x i j {\displaystyle x_{ij}} be the i independently drawn observation ( i =1,..., N ) on
3534-402: The sample mean, but the sample mean is slightly correlated with each observation since it is defined in terms of all observations. If the population mean E ( X ) {\displaystyle \operatorname {E} (\mathbf {X} )} is known, the analogous unbiased estimate using the population mean, has N {\displaystyle \textstyle N} in
3596-402: The simple n stands for the common alveolar nasal /n/ , an n with macron ( n̄ ) represents the velar nasal /ŋ/ ; the vowel ē stands for a (short) higher /ɪ/ by contrast with plain e /ɛ/ ; likewise ō /ʊ/ contrasts with plain o /ɔ/ . In Hiw orthography, the consonant r̄ stands for the prestopped velar lateral approximant /ᶢʟ/ . In Araki , the same symbol r̄ encodes
3658-412: The term or expression to be negated. For example: Common set theory notation: Electrical engineering notation: in which the times (cross) means multiplication, the dot means logical AND, and the plus sign means logical OR. Both illustrate De Morgan's laws and its mnemonic, "break the line, change the sign". In common logarithms , a bar over the characteristic indicates that it is negative—whilst
3720-455: The text) and strikethrough (a line through the text). Unicode includes two graphic characters , U+00AF ¯ MACRON and U+203E ‾ OVERLINE . They are compatibility equivalent to the U+0020 SPACE with non-spacing diacritics U+0304 ◌̄ COMBINING MACRON and U+0305 ◌̅ COMBINING OVERLINE respectively;
3782-562: The true mean. Thus the sample mean is a random variable , not a constant, and consequently has its own distribution. For a random sample of N observations on the j random variable, the sample mean's distribution itself has mean equal to the population mean E ( X j ) {\displaystyle E(X_{j})} and variance equal to σ j 2 / N {\displaystyle \sigma _{j}^{2}/N} , where σ j 2 {\displaystyle \sigma _{j}^{2}}
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#17327869101303844-649: The vinculum was used to group together symbols so that they could be treated as a unit. Today, parentheses are more commonly used for this purpose. The overline is used to indicate a sample mean : Survival functions or complementary cumulative distribution functions are often denoted by placing an overline over the symbol for the cumulative: F ¯ ( x ) = 1 − F ( x ) {\displaystyle {\overline {F}}(x)=1-F(x)} . In set theory and some electrical engineering contexts, negation operators (also known as complement ) can be written as an overline above
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