ISSN 2590-9770
The Art of Discrete and Applied Mathematics 3 (2020) #P2.08
https://doi.org/10.26493/2590-9770.1326.9fd
(Also available at http://adam-journal.eu)
On median and quartile sets of ordered random
variables*
Iztok Banič
Faculty of Natural Sciences and Mathematics, University of Maribor,
Koroška 160, SI-2000 Maribor, Slovenia, and
Institute of Mathematics, Physics and Mechanics,
Jadranska 19, SI-1000 Ljubljana, Slovenia, and
Andrej Marušič Institute, University of Primorska, Muzejski trg 2, SI-6000 Koper, Slovenia
Janez Žerovnik
Faculty of Mechanical Engineering, University of Ljubljana,
Aškerčeva 6, SI-1000 Ljubljana, Slovenia, and
Institute of Mathematics, Physics and Mechanics,
Jadranska 19, SI-1000 Ljubljana, Slovenia
Received 30 November 2018, accepted 13 August 2019, published online 21 August 2020
Abstract
We give new results about the set of all medians, the set of all first quartiles and the set
of all third quartiles of a finite dataset. We also give new and interesting results about rela-
tionships between these sets. We also use these results to provide an elementary correctness
proof of the Langford’s doubling method.
Keywords: Statistics, probability, median, first quartile, third quartile, median set, first quartile set,
third quartile set.
Math. Subj. Class.: 62-07, 60E05, 60-08, 60A05, 62A01
*This work was supported in part by the Slovenian Research Agency (grants J1-8155, N1-0071, P2-0248, and
J1-1693.)
E-mail addresses: iztok.banic@um.si (Iztok Banič), janez.zerovnik@fs.uni-lj.si (Janez Žerovnik)
cb This work is licensed under https://creativecommons.org/licenses/by/4.0/
ISSN 2590-9770
The Art of Discrete and Applied Mathematics 3 (2020) #P2.08
https://doi.org/10.26493/2590-9770.1326.9fd
(Dostopno tudi na http://adam-journal.eu)
O medianskih in kvartilnih množicah urejenih
slučajnih spremenljivk*
Iztok Banič
Fakulteta za naravoslovje in matematiko, Univerza v Mariboru,
Koroška 160, SI-2000 Maribor, Slovenija, in
Inštitut za matematiko, fiziko in mehaniko,
Jadranska 19, SI-1000 Ljubljana, Slovenija, in
Inštitut Andrej Marušič, Univerza na Primorskem, Muzejski trg 2, SI-6000 Koper,
Slovenija
Janez Žerovnik
Fakulteta za strojništvo, Univerza v Ljubljani,
Aškerčeva 6, SI-1000 Ljubljana, Slovenija, in
Inštitut za matematiko, fiziko in mehaniko,
Jadranska 19, SI-1000 Ljubljana, Slovenija
Prejeto 30. novembra 2018, sprejeto 13. avgusta 2019, objavljeno na spletu 21. avgusta 2020
Povzetek
Predstavimo nove rezultate o množici vseh median, množici vseh prvih kvartilov in
množici vseh tretjih kvartilov končnega nabora podatkov. Predstavimo tudi nove in za-
nimive rezultate o relacijah med temi množicami. Te rezultate uporabimo tudi za elemen-
tarni dokaz pravilnosti Langfordove podvojitvene metode.
Ključne besede: Statistika, verjetnost, mediana, prvi kvartil, tretji kvartil, medianska množica, množica
prvega kvartila, množica tretjega kvartila.
Math. Subj. Class.: 62-07, 60E05, 60-08, 60A05, 62A01
*To delo je bilo delno podprto s strani Javne agencije za raziskovalno dejavnost Republike Slovenije (dotacije
J1-8155, N1-0071, P2-0248 in J1-1693.)
E-poštna naslova: iztok.banic@um.si (Iztok Banič), janez.zerovnik@fs.uni-lj.si (Janez Žerovnik)
cb To delo je objavljeno pod licenco https://creativecommons.org/licenses/by/4.0/