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by handmodel 1487 days ago
Perhaps you are misunderstanding the records it is describing.

A record in that data is defined as a particular high in a particular city on a particular day. The data goes back 145 years in Los Angeles.

So if it is the hottest May 24th ever that would be a record.

If everyday followed an identical and uncorrelated distribution then we would expect that 1/145 days would be record.

In your IQ example imagine if you had a school with 365 separate classrooms with 144 students in each one. A new 145th student then enters each classroom. The chance that the new student is the one with the highest IQ is 1/145. So in the universe of the 365 classrooms you'd expect 2 new IQ records to be set.
1 comments
jedberg 1487 days ago
I fully understand what they record is.

Let me ask this, why in your school with 365 classrooms would you expect 2 new IQ records to be set with 145 new students. With a normal distribution, you'd expect all of those new students to be within one standard deviation of 100.

> The chance that the new student is the one with the highest IQ is 1/145

Why do you think this is the case?

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handmodel 1487 days ago
The student who enters the classroom has an IQ that follows the same distribution of intelligence of any of the other students. Therefore, one student out of the 145 must have the highest intelligence and the chances that it is student #4, #30, #100, or #145 is the same.

Here is some python code you can run. You can change around the distribution however you want and you'd get the same exact results. The chance that a particular record is the highest in a set of IID variables is not dependent on the distribution itself.

  from numpy import random
  RecordsSet=0
  TotalSimulations=365000
  for i in range(0,TotalSimulations):
      ClassRoomSample = random.normal(100, 15, 144)
      RecordIQ = max(ClassRoomSample)
      NewStudentIQ = random.normal(100, 15, 1)
      if NewStudentIQ>RecordIQ:
          RecordsSet=RecordsSet+1

  print(100*float(1)/145)
  print(100*float(RecordsSet)/TotalSimulations)
A record is set 1 out of every 145 days/classes. Which means in a year/school of 365 days/classes you'd expect a bit more than 2 records on average.
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