Monday, July 15, 2024

What is a semi-log plot and how can you use it for Covid data?

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Just to be clear, 106 means 10 x 10 x 10 x 10 x 10 x 10. But what if I want to do the inverse of 10 raised to a certain power? It is much easier to write large numbers by raising them to a certain power – this is exactly what we do with numbers in scientific notation. Finding the power of 10 that a number is high is exactly what a logarithm does. If I take the log of 1,000,000, that gives the result of 6. Oh, here’s an important note. If we are talking about 10 raised to a certain power, that means we are using a logarithmic base of 10. The two most common bases are 10 (because we write numbers in base 10) or e, the natural number where e is about 2.718 (this is irrational). Here is a more detailed explanation of th.

Illustration: Rhett Allain

But wait! You can also take the logarithm for numbers that are not whole powers of 10. Let’s just take a number – I’m going with 1,234. If I take the logarithm of that number, I get:

Illustration: Rhett Allain

This means that if you increase 10 to the power of 3.09132, you get 1234. But why? Why would you do that? OK, back to our terrible Covid data. Suppose instead of plotting the number of confirmed infections, I plot the log (base 10) of the number of infections. I can then plot the log of the number versus the number of days. Here is what it looks like.

To be clear, this is the same data as the first graph, but there is a big difference. You can actually see the data for South Korea even though the numbers for that country are much lower than the United States. Why? Well, let’s look at the total number of confirmed cases as of November 17, 2020. For the United States it is 11,036,935 and for South Korea it is 28,769. Now let’s take the log (base 10) of these two numbers. .


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