Quality & Quantity (2006) 40:145–156 © Springer 2006
Fuzziness and Bias in Decision-Making
Processes Using an Arithmetic Mean Criterion
, ZDENEK KUCEROVSKY
, WILLIAM D.
and GHEORGHE SILBERBERG
Department of Physics & Engineering, Murray State University, Murray, Kentucky,
Department of Electrical and Computer Engineering, University of Western Ontario,
Department of Economics, Central European University, Budapest,
Abstract. Grade averaging (by arithmetic mean) is often performed as an attempt to assess
overall student performance. In the case of grade comparison originating in non-equivalent
scales, rank errors and absurd averaging may result. As averages are sometimes used for
candidate selection, the paper dicusses how decisions based on arithmetic mean interpreta-
tion may be true, false, or fuzzy, according to different categories of participating candidates.
A two stage selection process is analyzed from the perspective of candidate categories. The
impact of the choice of asessment scale on the decision-making process is also evaluated and
statistical biases are identiﬁed. The relevance of using a uniformity criterion is demonstrated.
Key words: decision-making, candidate selection, educational measurement, ordinal scales,
letter grades, arithmetic mean, equivalent scales, average, grade conversion, uniformity
Selection is one of the main functions of marks (Natriello, 1992). Arith-
metic mean is extensively used for evaluating overall student performance.
The rank of average (deﬁned by thresholds for the arithmetic mean related
to the grading scales) is often employed in candidate selection. Particularly
in schools (but not only), such a process relies on the interpretation of the
measure given by the rank of (grade) average.
Measurement scales have been a continous topic of research and
debates. Stevens (1946; 1951) classiﬁed scales into nominal, ordinal, inter-
val, logarithmic interval, ratio, and absolute. There are other classiﬁcations
Address for correspondence: A. Ieta, Department of Physics & Engineering, Murray
State University, Murray, Kentucky, 42071, U.S.A. E-mail: firstname.lastname@example.org