## METHOD OF STATISTICAL ESTIMATION OF ACADEMIC COMPETITION AND TESTING TASKS RELATIVE COMPLEXITY

FSBEI HPE USPTU, Ufa, the Russian Federation

Khaybullin R.Y.

FSBEI HPE USPTU, Ufa, the Russian Federation

khayrya@mail.ru

This article deals with the problem of relative complexity problems estimation at the thematic competitions among pupils and students. The experience shows that the grades (in points) given by organizers for correct solving of problems do not often correspond the statistics given after inspection. The main difficulties here are connected with the problem that it’s impossible to give any formal ground, formulate a multipurpose criterion for such estimation. Even for academic school problems the correlation ratio between expert and statistical estimation may be less than 0.5. Nevertheless, adequate interrelationship of points and difficulties of solving mathematical problems facilitates more fair arranging of participants taking into account their knowledge and skills level, which is the main purpose of any test, academic competition, contest. The present work suggests the calculation method of the most adequate estimation. It is based on the results of the works of the conducted academic competition and therefore the results are considered to be of posteriori character. Two criteria of adequate estimation of complexity are formulated and relevant mathematic problems for each of them are given. The conducted analysis for specific academic competitions let us make conclusions concerning the correctness of problems relative estimation, the occurrence of insignificant problems among given etc. In particular, abundant number of problems are often offered at the academic competitions, but as a rule, complex problems are underestimated and easy ones are overestimated by organizers. Suggested methods are applied for any contests and tests on any subjects, both for pupils and students.

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complexity estimation; Lagrange function; posteriori analysis; thematic competitions; апостериорный анализ; оценка сложности; предметные олимпиады; функция Лагранжа DOI 10.17122/ogbus-2014-5-420-430 References to this article (GOST) Lazarev V.A., Khaybullin R.Y. METHOD OF STATISTICAL ESTIMATION OF ACADEMIC COMPETITION AND TESTING TASKS RELATIVE COMPLEXITY // Electronic scientific journal "Oil and Gas Business". 2014. №5. P.420-430. URL: http://ogbus.ru/issues/5_2014/ogbus_5_2014_p420-430_LazarevVA_ru.pdf