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Comment by jedberg | Hacker News Reader

I think your math is wrong. You wouldn't see two record highs every year with a normal distribution. The record high for each day would be set once, and would be an extreme outlier. Think about something like IQ. If you grab a group of people you wouldn't expect to find a genius every time, or even most of the time. Most of the time you'd expect to find someone near 100. Unless IQs had been steadily rising.

With a normal distribution you wouldn't expect even one record to be set every year. The expected case would be zero records in a year.

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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.

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?

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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