Shifting Marks with the Bell Curve


Don’t worry; we don’t do this sort of thing. We use criterion-referenced assessment, so your peers’ performance doesn’t affect your evaluation.

We looked at a question in class (page 431 #11) in which a professor was “belling” the marks. Madison asked if there were marks that would be shifted down as a result of the belling.

There are, sort of. Here’s the math.

Let’s call the original mark x_1 and the resultant mark x_2. We want to know for which values of x_1

x_2 \textless x_1

In the belling process the z-score is maintained for each grade; so

\frac{x_1-55}{13}=\frac{x_2-70}{10}

Solving for x_2 yields

x_2 = 10\left( \frac{x_1-55}{13} \right) + 70

Substituting into the inequality

x_2 \textless x_1

yields

x_1 \textgreater 120

which is, you know, impossible anyway. :)

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