Abstract
There are many different independent factors that affect student grades. There are many physical situations like this, in which many different independent factors affect a phenomenon, and in most such situations, we encounter normal distribution – in full accordance with the Central Limit Theorem, which explains that in such situations, distribution should be close to normal. However, the grade distribution is definitely not normal – it is multi-modal. In this paper, we explain this strange phenomenon, and, moreover, we explain several observed features of this multi-modal distribution.
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References
Belohlavek, R., Dauben, J.W., Klir, G.J.: Fuzzy Logic and Mathematics: A Historical Perspective. Oxford University Press, New York (2017)
Feynman, R., Leighton, R., Sands, M.: The Feynman Lectures on Physics. Addison Wesley, Boston (2005)
Finkelstein, A., Kosheleva, O., Kreinovich, V.: Astrogeometry: towards mathematical foundations. Int. J. Theor. Phys. 36(4), 1009–1020 (1997)
Finkelstein, A., Kosheleva, O., Kreinovich, V.: Astrogeometry: geometry explains shapes of celestial bodies. Geombinatorics VI(4), 125–139 (1997)
Jaulin, L., Kiefer, M., Didrit, O., Walter, E.: Applied Interval Analysis, with Examples in Parameter and State Estimation, Robust Control, and Robotics. Springer, London (2001)
Klir, G., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Prentice Hall, Upper Saddle River (1995)
Kreinovich, V., Lakeyev, A., Rohn, J., Kahl, P.: Computational Complexity and Feasibility of Data Processing and Interval Computations. Kluwer, Dordrecht (1998)
Li, S., Ogura, Y., Kreinovich, V.: Limit Theorems and Applications of Set Valued and Fuzzy Valued Random Variables. Kluwer Academic Publishers, Dordrecht (2002)
Mayer, G.: Interval Analysis and Automatic Result Verification. de Gruyter, Berlin (2017)
Mendel, J.M.: Uncertain Rule-Based Fuzzy Systems: Introduction and New Directions. Springer, Cham (2017)
Moore, R.E., Kearfott, R.B., Cloud, M.J.: Introduction to Interval Analysis. SIAM, Philadelphia (2009)
Rabinovich, S.G.: Measurement Errors and Uncertainties: Theory and Practice. Springer, New York (2005)
Nguyen, H.T., Kreinovich, V.: Nested intervals and sets: concepts, relations to fuzzy sets, and applications. In: Kearfott, R.B., Kreinovich, V. (eds.) Applications of Interval Computations, pp. 245–290. Kluwer, Dordrecht (1996)
Nguyen, H.T., Walker, C., Walker, E.A.: A First Course in Fuzzy Logic. Chapman and Hall/CRC, Boca Raton (2019)
Novák, V., Perfilieva, I., Močkoř, J.: Mathematical Principles of Fuzzy Logic. Kluwer, Boston, Dordrecht (1999)
Sheskin, D.J.: Handbook of Parametric and Nonparametric Statistical Procedures. Chapman and Hall/CRC, Boca Raton (2011)
Thorne, K.S., Blandford, R.D.: Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics. Princeton University Press, Princeton (2017)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Acknowledgments
This work was supported in part by the US National Science Foundation via grant HRD-1242122 (Cyber-ShARE Center of Excellence).
The authors are thankful to the anonymous referees for valuable suggestions.
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Kosheleva, O., Servin, C., Kreinovich, V. (2019). Why Grade Distribution Is Often Multi-modal: An Uncertainty-Based Explanation. In: Kearfott, R., Batyrshin, I., Reformat, M., Ceberio, M., Kreinovich, V. (eds) Fuzzy Techniques: Theory and Applications. IFSA/NAFIPS 2019 2019. Advances in Intelligent Systems and Computing, vol 1000. Springer, Cham. https://doi.org/10.1007/978-3-030-21920-8_10
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DOI: https://doi.org/10.1007/978-3-030-21920-8_10
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