Teaching and links

TEACHING

In the Spring of 2025 I am teaching:

• MATH-4520/5520 Introduction to Statistics

• MATH 4820/5820 History of Mathematical ideas

CU policies

Should exam grades follow normal distribution?

No. Why not? See what Wikipedia writes:

Common misconceptions

Studies have shown that the central limit theorem is subject to several common but serious misconceptions, some of which appear in widely used textbooks.[22][23][24]These include: 

• The misconceived belief that the theorem applies to random sampling of any variable, rather than to the mean values (or sums) of iid random variables extracted from a population by repeated sampling. That is, the theorem assumes the random sampling produces a sampling distribution formed from different values of means (or sums) of such random variables.

• The misconceived belief that the theorem ensures that random sampling leads to the emergence of a normal distribution for sufficiently large samples of any random variable, regardless of the population distribution. In reality, such sampling asymptotically reproduces the properties of the population, an intuitive result underpinned by the Glivenko-Cantelli theorem.

• The misconceived belief that the theorem leads to a good approximation of a normal distribution for sample sizes greater than around 30,[25] allowing reliable inferences regardless of the nature of the population. In reality, this empirical rule of thumb has no valid justification, and can lead to seriously flawed inferences. See Z-test for where the approximation holds.