In this video, we introduce the median and mean by asking, “Do you have more than the average number of feet?”
The example given is a sample of pedestrians, one of whom only has one foot due to cancer surgery. As a result, the
mean is less than the median. We show the process of calculating a median – by lining up the sample from smallest
to tallest – and of a mean – the arithmetic calculations – and emphasize that while someone typically has the median
level of some characteristic (e.g., 2 feet), often no-one has the mean level (e.g., 1.89 feet). This demonstrates the
difference between a calculated parameter (such as a mean) and one that can be directly observed (such as the
median). The video ends by discussing medical risk, arguing that because median risk is generally below mean risk
(often, a small number of individuals are at greatly increased risk), many of us get treatments or tests we don’t need.
This video fits in well in the introductory part of any statistics course because a) it covers basic subjects; b) it takes
something that seems quite trivial, means and medians, and then connects them to a concrete application,
overdiagnosis and overtreatment in the medicine. The video can be accompanied by Chapters 2 and 5 in What is a p-value
In the video, the statistician says that scientific statements have to be very precise and we have to think hard about whether they are true. This can lead to discussions about a. How precise is “very” precise? Should we say e.g., that the mean height of US men is 5’10” or would it be more “scientific” to say that it is 5’10.23416”?
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