Average (English Wikipedia)

Stack, Sue; Watson, Jane; Hindley, Sue; Samson, Pauline; Devlin, Robyn (2010). "What's average?". Australian Mathematics Teacher (AMT). 66 (3): 7–15. ISSN 0045-0685. Academia 48155690. EBSCOhost 53382428. Informit 10.3316/informit.354027435519820.

alwaraq.net (Global: low place; English: low place)

Medieval Arabic had عور ʿawr meaning "blind in one eye" and عوار ʿawār meant "any defect, or anything defective or damaged". Some medieval Arabic dictionaries are at Baheth.info Archived 2013-10-29 at the Wayback Machine, and some translation to English of what's in the medieval Arabic dictionaries is in Lane's Arabic-English Lexicon, pages 2193 and 2195. The medieval dictionaries do not list the word-form عوارية ʿawārīa. ʿAwārīa can be naturally formed in Arabic grammar to refer to things that have ʿawār, but in practice in medieval Arabic texts ʿawārīa is a rarity or non-existent, while the forms عواري ʿawārī and عوارة ʿawāra are frequently used when referring to things that have ʿawār or damage – this can be seen in the searchable collection of medieval texts at AlWaraq.net (book links are clickable on righthand side).

ams.org (Global: 434^th place; English: 249^th place)

mathscinet.ams.org

Narboux, Julien; Braun, David (2016). "Towards a certified version of the encyclopedia of triangle centers" (PDF). Mathematics in Computer Science. 10 (1): 57–73. doi:10.1007/s11786-016-0254-4. MR 3483261. under the guidance of Clark Kimberling, an electronic encyclopedia of triangle centers (ETC) has been developed, it contains more than 7000 centers and many properties of these points

amstat.org (Global: low place; English: 7,313^th place)

jse.amstat.org

Kaplan, Jennifer; Fisher, Dianne G.; Rogness, Neal T. (July 2010). "Lexical Ambiguity in Statistics: How students use and define the words: association, average, confidence, random and spread" [part 2] (PDF). Journal of Statistics Education. 18 (2). doi:10.1080/10691898.2010.11889491. eISSN 1069-1898.
Kaplan, Jennifer J.; Fisher, Diane G.; Rogness, Neal T. (2009). "Lexical Ambiguity in Statistics: What do students know about the words association, average, confidence, random and spread?" [part 1]. Journal of Statistics Education. 17 (3). doi:10.1080/10691898.2009.11889535. eISSN 1069-1898.

amstat.org

"Bakker, Arthur. "The early history of average values and implications for education." Journal of Statistics Education 11.1 (2003): 17-26". Archived from the original on 2015-12-04. Retrieved 2015-10-22.

archive.org (Global: 6^th place; English: 6^th place)

The Arabic origin of avaria was first reported by Reinhart Dozy in the 19th century. Dozy's original summary is in his 1869 book Glossaire. Summary information about the word's early records in Italian-Latin, Italian, Catalan, and French is at avarie @ CNRTL.fr Archived 2019-01-06 at the Wayback Machine. The seaport of Genoa is the location of the earliest-known record in European languages, year 1157. A set of medieval Latin records of avaria at Genoa is in the downloadable lexicon Vocabolario Ligure, by Sergio Aprosio, year 2001, avaria in Volume 1 pages 115-116. Many more records in medieval Latin at Genoa are at StoriaPatriaGenova.it, usually in the plurals avariis and avarias. At the port of Marseille in the 1st half of the 13th century notarized commercial contracts have dozens of instances of Latin avariis (ablative plural of avaria), as published in Blancard year 1884. Some information about the English word over the centuries is at NED (year 1888). See also the definition of English "average" in English dictionaries published in the early 18th century, i.e., in the time period just before the big transformation of the meaning: Kersey-Phillips' dictionary (1706), Blount's dictionary (1707 edition), Hatton's dictionary (1712), Bailey's dictionary (1726), Martin's dictionary (1749). Some complexities surrounding the English word's history are discussed in Hensleigh Wedgwood year 1882 page 11 and Walter Skeat year 1888 page 781. Today there is consensus that: (#1) today's English "average" descends from medieval Italian avaria, Catalan avaria, and (#2) among the Latins the word avaria started in the 12th century and it started as a term of Mediterranean sea-commerce, and (#3) there is no root for avaria to be found in Latin, and (#4) a substantial number of Arabic words entered Italian, Catalan and Provençal in the 12th and 13th centuries starting as terms of Mediterranean sea-commerce, and (#5) the Arabic ʿawār | ʿawārī is phonetically a good match for avaria, as conversion of w to v was regular in Latin and Italian, and -ia is a suffix in Italian, and the Western word's earliest records are in Italian-speaking locales (writing in Latin). And most commentators agree that (#6) the Arabic ʿawār | ʿawārī = "damage | relating to damage" is semantically a good match for avaria = "damage or damage expenses". A minority of commentators have been dubious about this on the grounds that the early records of Italian-Latin avaria have, in some cases, a meaning of "an expense" in a more general sense – see TLIO (in Italian). The majority view is that the meaning of "an expense" was an expansion from "damage and damage expense", and the chronological order of the meanings in the records supports this view, and the broad meaning "an expense" was never the most commonly used meaning. On the basis of the above points, the inferential step is made that the Latinate word came or probably came from the Arabic word.

baheth.info (Global: low place; English: low place)

Medieval Arabic had عور ʿawr meaning "blind in one eye" and عوار ʿawār meant "any defect, or anything defective or damaged". Some medieval Arabic dictionaries are at Baheth.info Archived 2013-10-29 at the Wayback Machine, and some translation to English of what's in the medieval Arabic dictionaries is in Lane's Arabic-English Lexicon, pages 2193 and 2195. The medieval dictionaries do not list the word-form عوارية ʿawārīa. ʿAwārīa can be naturally formed in Arabic grammar to refer to things that have ʿawār, but in practice in medieval Arabic texts ʿawārīa is a rarity or non-existent, while the forms عواري ʿawārī and عوارة ʿawāra are frequently used when referring to things that have ʿawār or damage – this can be seen in the searchable collection of medieval texts at AlWaraq.net (book links are clickable on righthand side).

books.google.com (Global: 3^rd place; English: 3^rd place)

The Arabic origin of avaria was first reported by Reinhart Dozy in the 19th century. Dozy's original summary is in his 1869 book Glossaire. Summary information about the word's early records in Italian-Latin, Italian, Catalan, and French is at avarie @ CNRTL.fr Archived 2019-01-06 at the Wayback Machine. The seaport of Genoa is the location of the earliest-known record in European languages, year 1157. A set of medieval Latin records of avaria at Genoa is in the downloadable lexicon Vocabolario Ligure, by Sergio Aprosio, year 2001, avaria in Volume 1 pages 115-116. Many more records in medieval Latin at Genoa are at StoriaPatriaGenova.it, usually in the plurals avariis and avarias. At the port of Marseille in the 1st half of the 13th century notarized commercial contracts have dozens of instances of Latin avariis (ablative plural of avaria), as published in Blancard year 1884. Some information about the English word over the centuries is at NED (year 1888). See also the definition of English "average" in English dictionaries published in the early 18th century, i.e., in the time period just before the big transformation of the meaning: Kersey-Phillips' dictionary (1706), Blount's dictionary (1707 edition), Hatton's dictionary (1712), Bailey's dictionary (1726), Martin's dictionary (1749). Some complexities surrounding the English word's history are discussed in Hensleigh Wedgwood year 1882 page 11 and Walter Skeat year 1888 page 781. Today there is consensus that: (#1) today's English "average" descends from medieval Italian avaria, Catalan avaria, and (#2) among the Latins the word avaria started in the 12th century and it started as a term of Mediterranean sea-commerce, and (#3) there is no root for avaria to be found in Latin, and (#4) a substantial number of Arabic words entered Italian, Catalan and Provençal in the 12th and 13th centuries starting as terms of Mediterranean sea-commerce, and (#5) the Arabic ʿawār | ʿawārī is phonetically a good match for avaria, as conversion of w to v was regular in Latin and Italian, and -ia is a suffix in Italian, and the Western word's earliest records are in Italian-speaking locales (writing in Latin). And most commentators agree that (#6) the Arabic ʿawār | ʿawārī = "damage | relating to damage" is semantically a good match for avaria = "damage or damage expenses". A minority of commentators have been dubious about this on the grounds that the early records of Italian-Latin avaria have, in some cases, a meaning of "an expense" in a more general sense – see TLIO (in Italian). The majority view is that the meaning of "an expense" was an expansion from "damage and damage expense", and the chronological order of the meanings in the records supports this view, and the broad meaning "an expense" was never the most commonly used meaning. On the basis of the above points, the inferential step is made that the Latinate word came or probably came from the Arabic word.
Underhill, L.G.; Bradfield d. (1998) Introstat, Juta and Company Ltd. ISBN 0-7021-3838-X p. 181
Djukić, Dušan; Janković, Vladimir; Matić, Ivan; Petrović, Nikola (2011-05-05). The IMO Compendium: A Collection of Problems Suggested for The International Mathematical Olympiads: 1959-2009 Second Edition. Springer Science & Business Media. ISBN 978-1-4419-9854-5.

britannica.com (Global: 37^th place; English: 64^th place)

"Mean | mathematics". Encyclopedia Britannica. Retrieved 2020-08-21.

cnr.it (Global: 5,792^nd place; English: 9,778^th place)

tlio.ovi.cnr.it

The Arabic origin of avaria was first reported by Reinhart Dozy in the 19th century. Dozy's original summary is in his 1869 book Glossaire. Summary information about the word's early records in Italian-Latin, Italian, Catalan, and French is at avarie @ CNRTL.fr Archived 2019-01-06 at the Wayback Machine. The seaport of Genoa is the location of the earliest-known record in European languages, year 1157. A set of medieval Latin records of avaria at Genoa is in the downloadable lexicon Vocabolario Ligure, by Sergio Aprosio, year 2001, avaria in Volume 1 pages 115-116. Many more records in medieval Latin at Genoa are at StoriaPatriaGenova.it, usually in the plurals avariis and avarias. At the port of Marseille in the 1st half of the 13th century notarized commercial contracts have dozens of instances of Latin avariis (ablative plural of avaria), as published in Blancard year 1884. Some information about the English word over the centuries is at NED (year 1888). See also the definition of English "average" in English dictionaries published in the early 18th century, i.e., in the time period just before the big transformation of the meaning: Kersey-Phillips' dictionary (1706), Blount's dictionary (1707 edition), Hatton's dictionary (1712), Bailey's dictionary (1726), Martin's dictionary (1749). Some complexities surrounding the English word's history are discussed in Hensleigh Wedgwood year 1882 page 11 and Walter Skeat year 1888 page 781. Today there is consensus that: (#1) today's English "average" descends from medieval Italian avaria, Catalan avaria, and (#2) among the Latins the word avaria started in the 12th century and it started as a term of Mediterranean sea-commerce, and (#3) there is no root for avaria to be found in Latin, and (#4) a substantial number of Arabic words entered Italian, Catalan and Provençal in the 12th and 13th centuries starting as terms of Mediterranean sea-commerce, and (#5) the Arabic ʿawār | ʿawārī is phonetically a good match for avaria, as conversion of w to v was regular in Latin and Italian, and -ia is a suffix in Italian, and the Western word's earliest records are in Italian-speaking locales (writing in Latin). And most commentators agree that (#6) the Arabic ʿawār | ʿawārī = "damage | relating to damage" is semantically a good match for avaria = "damage or damage expenses". A minority of commentators have been dubious about this on the grounds that the early records of Italian-Latin avaria have, in some cases, a meaning of "an expense" in a more general sense – see TLIO (in Italian). The majority view is that the meaning of "an expense" was an expansion from "damage and damage expense", and the chronological order of the meanings in the records supports this view, and the broad meaning "an expense" was never the most commonly used meaning. On the basis of the above points, the inferential step is made that the Latinate word came or probably came from the Arabic word.

cnrtl.fr (Global: 938^th place; English: 6,622^nd place)

The Arabic origin of avaria was first reported by Reinhart Dozy in the 19th century. Dozy's original summary is in his 1869 book Glossaire. Summary information about the word's early records in Italian-Latin, Italian, Catalan, and French is at avarie @ CNRTL.fr Archived 2019-01-06 at the Wayback Machine. The seaport of Genoa is the location of the earliest-known record in European languages, year 1157. A set of medieval Latin records of avaria at Genoa is in the downloadable lexicon Vocabolario Ligure, by Sergio Aprosio, year 2001, avaria in Volume 1 pages 115-116. Many more records in medieval Latin at Genoa are at StoriaPatriaGenova.it, usually in the plurals avariis and avarias. At the port of Marseille in the 1st half of the 13th century notarized commercial contracts have dozens of instances of Latin avariis (ablative plural of avaria), as published in Blancard year 1884. Some information about the English word over the centuries is at NED (year 1888). See also the definition of English "average" in English dictionaries published in the early 18th century, i.e., in the time period just before the big transformation of the meaning: Kersey-Phillips' dictionary (1706), Blount's dictionary (1707 edition), Hatton's dictionary (1712), Bailey's dictionary (1726), Martin's dictionary (1749). Some complexities surrounding the English word's history are discussed in Hensleigh Wedgwood year 1882 page 11 and Walter Skeat year 1888 page 781. Today there is consensus that: (#1) today's English "average" descends from medieval Italian avaria, Catalan avaria, and (#2) among the Latins the word avaria started in the 12th century and it started as a term of Mediterranean sea-commerce, and (#3) there is no root for avaria to be found in Latin, and (#4) a substantial number of Arabic words entered Italian, Catalan and Provençal in the 12th and 13th centuries starting as terms of Mediterranean sea-commerce, and (#5) the Arabic ʿawār | ʿawārī is phonetically a good match for avaria, as conversion of w to v was regular in Latin and Italian, and -ia is a suffix in Italian, and the Western word's earliest records are in Italian-speaking locales (writing in Latin). And most commentators agree that (#6) the Arabic ʿawār | ʿawārī = "damage | relating to damage" is semantically a good match for avaria = "damage or damage expenses". A minority of commentators have been dubious about this on the grounds that the early records of Italian-Latin avaria have, in some cases, a meaning of "an expense" in a more general sense – see TLIO (in Italian). The majority view is that the meaning of "an expense" was an expansion from "damage and damage expense", and the chronological order of the meanings in the records supports this view, and the broad meaning "an expense" was never the most commonly used meaning. On the basis of the above points, the inferential step is made that the Latinate word came or probably came from the Arabic word.

conceptstew.co.uk (Global: low place; English: low place)

"Mean or median? 'Average' household income". Statistics for the Terrified. Concept Stew Ltd. 4 April 2005. Archived from the original on 2005-12-05.

dictionary.com (Global: 1,672^nd place; English: 1,248^th place)

"average". Dictionary.com Unabridged (Online). n.d. Retrieved 2023-05-25.

doi.org (Global: 2^nd place; English: 2^nd place)

Kaplan, Jennifer; Fisher, Dianne G.; Rogness, Neal T. (July 2010). "Lexical Ambiguity in Statistics: How students use and define the words: association, average, confidence, random and spread" [part 2] (PDF). Journal of Statistics Education. 18 (2). doi:10.1080/10691898.2010.11889491. eISSN 1069-1898.
Watson, Jane M. (May 2007). "The Role of Cognitive Conflict in Developing Students' Understanding of Average". Educational Studies in Mathematics. 65: 21–47. doi:10.1007/s10649-006-9043-3. ISSN 0013-1954.
Kaplan, Jennifer J.; Fisher, Diane G.; Rogness, Neal T. (2009). "Lexical Ambiguity in Statistics: What do students know about the words association, average, confidence, random and spread?" [part 1]. Journal of Statistics Education. 17 (3). doi:10.1080/10691898.2009.11889535. eISSN 1069-1898.
Bibby, John (1974). "Axiomatisations of the average and a further generalisation of monotonic sequences". Glasgow Mathematical Journal. 15: 63–65. doi:10.1017/s0017089500002135.
Narboux, Julien; Braun, David (2016). "Towards a certified version of the encyclopedia of triangle centers" (PDF). Mathematics in Computer Science. 10 (1): 57–73. doi:10.1007/s11786-016-0254-4. MR 3483261. under the guidance of Clark Kimberling, an electronic encyclopedia of triangle centers (ETC) has been developed, it contains more than 7000 centers and many properties of these points
Plackett, R. L. (1958). "Studies in the History of Probability and Statistics: VII. The Principle of the Arithmetic Mean". Biometrika. 45 (1/2): 130–135. doi:10.2307/2333051. JSTOR 2333051.
Libertz, Daniel (2018-12-31). "Framed for Lying: Statistics as In/Artistic Proof". Res Rhetorica. 5 (4). doi:10.29107/rr2018.4.1. ISSN 2392-3113.

ebscohost.com (Global: 1,433^rd place; English: 739^th place)

search.ebscohost.com

Stack, Sue; Watson, Jane; Hindley, Sue; Samson, Pauline; Devlin, Robyn (2010). "What's average?". Australian Mathematics Teacher (AMT). 66 (3): 7–15. ISSN 0045-0685. Academia 48155690. EBSCOhost 53382428. Informit 10.3316/informit.354027435519820.
Quinnell, Lorna (September 2017). "Those muddling M's: Scaffolding understanding of averages in mathematics". The Australian Mathematics Teacher (AMT). 73 (3): 6–12. ISSN 0045-0685. EBSCOhost 125324609. Informit 10.3316/informit.123380293707263, 10.3316/aeipt.218997.
de Mestre, Neville (2019). "discovery: What do you mean by an average?". Australian Mathematics Education Journal (AMEJ). 1 (4): 24–25. ISSN 2652-0176. EBSCOhost 140411813. Informit 10.3316/informit.837688193205822.

ed.gov (Global: 318^th place; English: 138^th place)

eric.ed.gov

Watson, Jane M.; Moritz, Jonathan B. (1999). "The Development of Concepts of Average". Focus on Learning Problems in Mathematics. 21 (4): 15–39. ISSN 0272-8893. ERIC EJ612005.
Watson, Jane; Chick, Helen (July 2–6, 2012). Average Revisited in Context. 35th Annual Meeting of the Mathematics Education Research Group of Australasia (MERGA), Singapore. Adelaide SA, Australia: Mathematics Education Research Group of Australasia. pp. 753–760. This research was partially funded by ARC Linkage Grant No. LP0669106.

files.wordpress.com (Global: 965^th place; English: 868^th place)

arcaneknowledgeofthedeep.files.wordpress.com

"Waterfield, Robin. "The theology of arithmetic." On the Mystical, mathematical and Cosmological Symbolism of the First Ten Number (1988). page 70" (PDF). Archived from the original (PDF) on 2016-03-04. Retrieved 2018-11-27.

hathitrust.org (Global: 296^th place; English: 153^rd place)

babel.hathitrust.org

Nagumo, Mitio (1930) [Eingegangen am 1. November, 1929]. "9. Über eine Klasse der Mittelwerte". Japanese Journal of Mathematics. VII: 71–79. HathiTrust record 006954247, items inu.30000091433023, uc1.31822020414991, rul.39030029662022.
Ray, John (1674). A Collection of English Words not Generally Used. London: H. Bruges. Retrieved 18 May 2015.

catalog.hathitrust.org

Nagumo, Mitio (1930) [Eingegangen am 1. November, 1929]. "9. Über eine Klasse der Mittelwerte". Japanese Journal of Mathematics. VII: 71–79. HathiTrust record 006954247, items inu.30000091433023, uc1.31822020414991, rul.39030029662022.

iase-web.org (Global: low place; English: low place)

Landtblom, Karin (July 2018). Sorto, M. A.; White, A.; Guyot, L. (eds.). IS DATA A QUANTITATIVE THING? AN ANALYSIS OF THE CONCEPT OF THE MODE IN TEXTBOOKS FOR GRADE 4-6 (PDF). Tenth International Conference on Teaching Statistics (ICOTS10), Kyoto, Japan. Looking back, looking forward. Voorburg, The Netherlands: International Statistical Institute. Archived from the original (PDF) on 2019-12-18.

informit.org (Global: low place; English: 7,651^st place)

search.informit.org

Stack, Sue; Watson, Jane; Hindley, Sue; Samson, Pauline; Devlin, Robyn (2010). "What's average?". Australian Mathematics Teacher (AMT). 66 (3): 7–15. ISSN 0045-0685. Academia 48155690. EBSCOhost 53382428. Informit 10.3316/informit.354027435519820.
Quinnell, Lorna (September 2017). "Those muddling M's: Scaffolding understanding of averages in mathematics". The Australian Mathematics Teacher (AMT). 73 (3): 6–12. ISSN 0045-0685. EBSCOhost 125324609. Informit 10.3316/informit.123380293707263, 10.3316/aeipt.218997.
de Mestre, Neville (2019). "discovery: What do you mean by an average?". Australian Mathematics Education Journal (AMEJ). 1 (4): 24–25. ISSN 2652-0176. EBSCOhost 140411813. Informit 10.3316/informit.837688193205822.

inria.fr (Global: 6,372^nd place; English: 5,582^nd place)

hal.inria.fr

Narboux, Julien; Braun, David (2016). "Towards a certified version of the encyclopedia of triangle centers" (PDF). Mathematics in Computer Science. 10 (1): 57–73. doi:10.1007/s11786-016-0254-4. MR 3483261. under the guidance of Clark Kimberling, an electronic encyclopedia of triangle centers (ETC) has been developed, it contains more than 7000 centers and many properties of these points

jst.go.jp (Global: 1,248^th place; English: 1,827^th place)

jstage.jst.go.jp

Nagumo, Mitio (1930) [Eingegangen am 1. November, 1929]. "9. Über eine Klasse der Mittelwerte". Japanese Journal of Mathematics. VII: 71–79. HathiTrust record 006954247, items inu.30000091433023, uc1.31822020414991, rul.39030029662022.

jstor.org (Global: 23^rd place; English: 15^th place)

Plackett, R. L. (1958). "Studies in the History of Probability and Statistics: VII. The Principle of the Arithmetic Mean". Biometrika. 45 (1/2): 130–135. doi:10.2307/2333051. JSTOR 2333051.

mercurynie.com.au (Global: low place; English: low place)

"Teacher Discussion - Meet the Averages" [based on an article in The Mercury, Sunday, 16 August, 1998, p.9]. Numeracy in the News. Archived from the original on 2011-03-01.

nytimes.com (Global: 7^th place; English: 7^th place)

Fowler, Elizabeth M. (August 4, 1956). "The Three Averages: A Study of How and Why Statisticians Make Use of Mean, Median and Mode / 3 AVERAGES USED BY STATISTICIANS". New York Times. pp. 19, 25 [but digitally tagged as 28, 34]. ProQuest 113794286.

oed.com (Global: 743^rd place; English: 419^th place)

"average, n.2". Oxford English Dictionary (online ed.). Oxford University Press. September 2019. Retrieved September 5, 2019. (Subscription or participating institution membership required.)

pageplace.de (Global: low place; English: low place)

api.pageplace.de

Triola, Mario F. (2014). Elementary Statistics (PDF) (12th Pearson New International ed.). Pearson Education Limited. p. 53. ISBN 978-1-292-03941-1.

proquest.com (Global: 121^st place; English: 59^th place)

Fowler, Elizabeth M. (August 4, 1956). "The Three Averages: A Study of How and Why Statisticians Make Use of Mean, Median and Mode / 3 AVERAGES USED BY STATISTICIANS". New York Times. pp. 19, 25 [but digitally tagged as 28, 34]. ProQuest 113794286.

resrhetorica.com (Global: low place; English: low place)

Libertz, Daniel (2018-12-31). "Framed for Lying: Statistics as In/Artistic Proof". Res Rhetorica. 5 (4). doi:10.29107/rr2018.4.1. ISSN 2392-3113.

springer.com (Global: 182^nd place; English: 172^nd place)

link.springer.com

Watson, Jane M. (May 2007). "The Role of Cognitive Conflict in Developing Students' Understanding of Average". Educational Studies in Mathematics. 65: 21–47. doi:10.1007/s10649-006-9043-3. ISSN 0013-1954.

storiapatriagenova.it (Global: low place; English: low place)

The Arabic origin of avaria was first reported by Reinhart Dozy in the 19th century. Dozy's original summary is in his 1869 book Glossaire. Summary information about the word's early records in Italian-Latin, Italian, Catalan, and French is at avarie @ CNRTL.fr Archived 2019-01-06 at the Wayback Machine. The seaport of Genoa is the location of the earliest-known record in European languages, year 1157. A set of medieval Latin records of avaria at Genoa is in the downloadable lexicon Vocabolario Ligure, by Sergio Aprosio, year 2001, avaria in Volume 1 pages 115-116. Many more records in medieval Latin at Genoa are at StoriaPatriaGenova.it, usually in the plurals avariis and avarias. At the port of Marseille in the 1st half of the 13th century notarized commercial contracts have dozens of instances of Latin avariis (ablative plural of avaria), as published in Blancard year 1884. Some information about the English word over the centuries is at NED (year 1888). See also the definition of English "average" in English dictionaries published in the early 18th century, i.e., in the time period just before the big transformation of the meaning: Kersey-Phillips' dictionary (1706), Blount's dictionary (1707 edition), Hatton's dictionary (1712), Bailey's dictionary (1726), Martin's dictionary (1749). Some complexities surrounding the English word's history are discussed in Hensleigh Wedgwood year 1882 page 11 and Walter Skeat year 1888 page 781. Today there is consensus that: (#1) today's English "average" descends from medieval Italian avaria, Catalan avaria, and (#2) among the Latins the word avaria started in the 12th century and it started as a term of Mediterranean sea-commerce, and (#3) there is no root for avaria to be found in Latin, and (#4) a substantial number of Arabic words entered Italian, Catalan and Provençal in the 12th and 13th centuries starting as terms of Mediterranean sea-commerce, and (#5) the Arabic ʿawār | ʿawārī is phonetically a good match for avaria, as conversion of w to v was regular in Latin and Italian, and -ia is a suffix in Italian, and the Western word's earliest records are in Italian-speaking locales (writing in Latin). And most commentators agree that (#6) the Arabic ʿawār | ʿawārī = "damage | relating to damage" is semantically a good match for avaria = "damage or damage expenses". A minority of commentators have been dubious about this on the grounds that the early records of Italian-Latin avaria have, in some cases, a meaning of "an expense" in a more general sense – see TLIO (in Italian). The majority view is that the meaning of "an expense" was an expansion from "damage and damage expense", and the chronological order of the meanings in the records supports this view, and the broad meaning "an expense" was never the most commonly used meaning. On the basis of the above points, the inferential step is made that the Latinate word came or probably came from the Arabic word.

storiapatriasavona.it (Global: low place; English: low place)

The Arabic origin of avaria was first reported by Reinhart Dozy in the 19th century. Dozy's original summary is in his 1869 book Glossaire. Summary information about the word's early records in Italian-Latin, Italian, Catalan, and French is at avarie @ CNRTL.fr Archived 2019-01-06 at the Wayback Machine. The seaport of Genoa is the location of the earliest-known record in European languages, year 1157. A set of medieval Latin records of avaria at Genoa is in the downloadable lexicon Vocabolario Ligure, by Sergio Aprosio, year 2001, avaria in Volume 1 pages 115-116. Many more records in medieval Latin at Genoa are at StoriaPatriaGenova.it, usually in the plurals avariis and avarias. At the port of Marseille in the 1st half of the 13th century notarized commercial contracts have dozens of instances of Latin avariis (ablative plural of avaria), as published in Blancard year 1884. Some information about the English word over the centuries is at NED (year 1888). See also the definition of English "average" in English dictionaries published in the early 18th century, i.e., in the time period just before the big transformation of the meaning: Kersey-Phillips' dictionary (1706), Blount's dictionary (1707 edition), Hatton's dictionary (1712), Bailey's dictionary (1726), Martin's dictionary (1749). Some complexities surrounding the English word's history are discussed in Hensleigh Wedgwood year 1882 page 11 and Walter Skeat year 1888 page 781. Today there is consensus that: (#1) today's English "average" descends from medieval Italian avaria, Catalan avaria, and (#2) among the Latins the word avaria started in the 12th century and it started as a term of Mediterranean sea-commerce, and (#3) there is no root for avaria to be found in Latin, and (#4) a substantial number of Arabic words entered Italian, Catalan and Provençal in the 12th and 13th centuries starting as terms of Mediterranean sea-commerce, and (#5) the Arabic ʿawār | ʿawārī is phonetically a good match for avaria, as conversion of w to v was regular in Latin and Italian, and -ia is a suffix in Italian, and the Western word's earliest records are in Italian-speaking locales (writing in Latin). And most commentators agree that (#6) the Arabic ʿawār | ʿawārī = "damage | relating to damage" is semantically a good match for avaria = "damage or damage expenses". A minority of commentators have been dubious about this on the grounds that the early records of Italian-Latin avaria have, in some cases, a meaning of "an expense" in a more general sense – see TLIO (in Italian). The majority view is that the meaning of "an expense" was an expansion from "damage and damage expense", and the chronological order of the meanings in the records supports this view, and the broad meaning "an expense" was never the most commonly used meaning. On the basis of the above points, the inferential step is made that the Latinate word came or probably came from the Arabic word.

tumblr.com (Global: 1,119^th place; English: 796^th place)

apstatsreview.tumblr.com

"AP Statistics Review - Density Curves and the Normal Distributions". Archived from the original on 2 April 2015. Retrieved 16 March 2015.

web.archive.org (Global: 1^st place; English: 1^st place)

Medieval Arabic had عور ʿawr meaning "blind in one eye" and عوار ʿawār meant "any defect, or anything defective or damaged". Some medieval Arabic dictionaries are at Baheth.info Archived 2013-10-29 at the Wayback Machine, and some translation to English of what's in the medieval Arabic dictionaries is in Lane's Arabic-English Lexicon, pages 2193 and 2195. The medieval dictionaries do not list the word-form عوارية ʿawārīa. ʿAwārīa can be naturally formed in Arabic grammar to refer to things that have ʿawār, but in practice in medieval Arabic texts ʿawārīa is a rarity or non-existent, while the forms عواري ʿawārī and عوارة ʿawāra are frequently used when referring to things that have ʿawār or damage – this can be seen in the searchable collection of medieval texts at AlWaraq.net (book links are clickable on righthand side).
The Arabic origin of avaria was first reported by Reinhart Dozy in the 19th century. Dozy's original summary is in his 1869 book Glossaire. Summary information about the word's early records in Italian-Latin, Italian, Catalan, and French is at avarie @ CNRTL.fr Archived 2019-01-06 at the Wayback Machine. The seaport of Genoa is the location of the earliest-known record in European languages, year 1157. A set of medieval Latin records of avaria at Genoa is in the downloadable lexicon Vocabolario Ligure, by Sergio Aprosio, year 2001, avaria in Volume 1 pages 115-116. Many more records in medieval Latin at Genoa are at StoriaPatriaGenova.it, usually in the plurals avariis and avarias. At the port of Marseille in the 1st half of the 13th century notarized commercial contracts have dozens of instances of Latin avariis (ablative plural of avaria), as published in Blancard year 1884. Some information about the English word over the centuries is at NED (year 1888). See also the definition of English "average" in English dictionaries published in the early 18th century, i.e., in the time period just before the big transformation of the meaning: Kersey-Phillips' dictionary (1706), Blount's dictionary (1707 edition), Hatton's dictionary (1712), Bailey's dictionary (1726), Martin's dictionary (1749). Some complexities surrounding the English word's history are discussed in Hensleigh Wedgwood year 1882 page 11 and Walter Skeat year 1888 page 781. Today there is consensus that: (#1) today's English "average" descends from medieval Italian avaria, Catalan avaria, and (#2) among the Latins the word avaria started in the 12th century and it started as a term of Mediterranean sea-commerce, and (#3) there is no root for avaria to be found in Latin, and (#4) a substantial number of Arabic words entered Italian, Catalan and Provençal in the 12th and 13th centuries starting as terms of Mediterranean sea-commerce, and (#5) the Arabic ʿawār | ʿawārī is phonetically a good match for avaria, as conversion of w to v was regular in Latin and Italian, and -ia is a suffix in Italian, and the Western word's earliest records are in Italian-speaking locales (writing in Latin). And most commentators agree that (#6) the Arabic ʿawār | ʿawārī = "damage | relating to damage" is semantically a good match for avaria = "damage or damage expenses". A minority of commentators have been dubious about this on the grounds that the early records of Italian-Latin avaria have, in some cases, a meaning of "an expense" in a more general sense – see TLIO (in Italian). The majority view is that the meaning of "an expense" was an expansion from "damage and damage expense", and the chronological order of the meanings in the records supports this view, and the broad meaning "an expense" was never the most commonly used meaning. On the basis of the above points, the inferential step is made that the Latinate word came or probably came from the Arabic word.
"Mean or median? 'Average' household income". Statistics for the Terrified. Concept Stew Ltd. 4 April 2005. Archived from the original on 2005-12-05.
"Teacher Discussion - Meet the Averages" [based on an article in The Mercury, Sunday, 16 August, 1998, p.9]. Numeracy in the News. Archived from the original on 2011-03-01.
Landtblom, Karin (July 2018). Sorto, M. A.; White, A.; Guyot, L. (eds.). IS DATA A QUANTITATIVE THING? AN ANALYSIS OF THE CONCEPT OF THE MODE IN TEXTBOOKS FOR GRADE 4-6 (PDF). Tenth International Conference on Teaching Statistics (ICOTS10), Kyoto, Japan. Looking back, looking forward. Voorburg, The Netherlands: International Statistical Institute. Archived from the original (PDF) on 2019-12-18.
"AP Statistics Review - Density Curves and the Normal Distributions". Archived from the original on 2 April 2015. Retrieved 16 March 2015.
"Bakker, Arthur. "The early history of average values and implications for education." Journal of Statistics Education 11.1 (2003): 17-26". Archived from the original on 2015-12-04. Retrieved 2015-10-22.
"Waterfield, Robin. "The theology of arithmetic." On the Mystical, mathematical and Cosmological Symbolism of the First Ten Number (1988). page 70" (PDF). Archived from the original (PDF) on 2016-03-04. Retrieved 2018-11-27.

wolfram.com (Global: 1,091^st place; English: 1,169^th place)

mathworld.wolfram.com

Cantrell, David W. "Pythagorean Means". MathWorld. Retrieved 2025-11-04.
Weisstein, Eric W. "Population Mean". mathworld.wolfram.com. Retrieved 2020-08-21.

worldcat.org (Global: 4^th place; English: 4^th place)

search.worldcat.org

Kaplan, Jennifer; Fisher, Dianne G.; Rogness, Neal T. (July 2010). "Lexical Ambiguity in Statistics: How students use and define the words: association, average, confidence, random and spread" [part 2] (PDF). Journal of Statistics Education. 18 (2). doi:10.1080/10691898.2010.11889491. eISSN 1069-1898.
Stack, Sue; Watson, Jane; Hindley, Sue; Samson, Pauline; Devlin, Robyn (2010). "What's average?". Australian Mathematics Teacher (AMT). 66 (3): 7–15. ISSN 0045-0685. Academia 48155690. EBSCOhost 53382428. Informit 10.3316/informit.354027435519820.
Quinnell, Lorna (September 2017). "Those muddling M's: Scaffolding understanding of averages in mathematics". The Australian Mathematics Teacher (AMT). 73 (3): 6–12. ISSN 0045-0685. EBSCOhost 125324609. Informit 10.3316/informit.123380293707263, 10.3316/aeipt.218997.
Watson, Jane M.; Moritz, Jonathan B. (1999). "The Development of Concepts of Average". Focus on Learning Problems in Mathematics. 21 (4): 15–39. ISSN 0272-8893. ERIC EJ612005.
Watson, Jane M. (May 2007). "The Role of Cognitive Conflict in Developing Students' Understanding of Average". Educational Studies in Mathematics. 65: 21–47. doi:10.1007/s10649-006-9043-3. ISSN 0013-1954.
Kaplan, Jennifer J.; Fisher, Diane G.; Rogness, Neal T. (2009). "Lexical Ambiguity in Statistics: What do students know about the words association, average, confidence, random and spread?" [part 1]. Journal of Statistics Education. 17 (3). doi:10.1080/10691898.2009.11889535. eISSN 1069-1898.
de Mestre, Neville (2019). "discovery: What do you mean by an average?". Australian Mathematics Education Journal (AMEJ). 1 (4): 24–25. ISSN 2652-0176. EBSCOhost 140411813. Informit 10.3316/informit.837688193205822.
Merigo, Jose M.; Cananovas, Montserrat (2009). "The Generalized Hybrid Averaging Operator and its Application in Decision Making". Journal of Quantitative Methods for Economics and Business Administration. 9: 69–84. ISSN 1886-516X.
Libertz, Daniel (2018-12-31). "Framed for Lying: Statistics as In/Artistic Proof". Res Rhetorica. 5 (4). doi:10.29107/rr2018.4.1. ISSN 2392-3113.

york.ac.uk (Global: 7,811^th place; English: 4,790^th place)

Eisenhart, Churchill. "The development of the concept of the best mean of a set of measurements from antiquity to the present day." Unpublished presidential address, American Statistical Association, 131st Annual Meeting, Fort Collins, Colorado. 1971.

youtube.com (Global: 13^th place; English: 14^th place)

Why Few Math Students Actually Understand the Meaning of Means (YouTube video). Math The World. 2024-08-27. Retrieved 2024-09-10.

yulghun.com (Global: low place; English: low place)

dict.yulghun.com

Medieval Arabic had عور ʿawr meaning "blind in one eye" and عوار ʿawār meant "any defect, or anything defective or damaged". Some medieval Arabic dictionaries are at Baheth.info Archived 2013-10-29 at the Wayback Machine, and some translation to English of what's in the medieval Arabic dictionaries is in Lane's Arabic-English Lexicon, pages 2193 and 2195. The medieval dictionaries do not list the word-form عوارية ʿawārīa. ʿAwārīa can be naturally formed in Arabic grammar to refer to things that have ʿawār, but in practice in medieval Arabic texts ʿawārīa is a rarity or non-existent, while the forms عواري ʿawārī and عوارة ʿawāra are frequently used when referring to things that have ʿawār or damage – this can be seen in the searchable collection of medieval texts at AlWaraq.net (book links are clickable on righthand side).

Average (English Wikipedia)

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