### What is a ratio?

When doing data science, understanding the concept of ratio can be useful. We use ratios to mean how much of something there is for a certain amount of another thing. For example, in a pair of shoes there is one shoe for each foot, so there is a ratio of 1 to 1. If you happen to have lots of pairs of shoes, say 48 pairs, the ratio between your 94 shoes and your two feet is indeed 48 shoes for each 1 foot.

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Ratios are usually expressed like a:b and are read 'a to b' or 'there are a units for each b units.' So, the ratio between shoes and feet would be 48:1 (forty-eight to one) because you have 48 left shoes and 48 right shoes, that is, 48 shoes for each one of your feet.

The women:men ratio in the world is roughly 52:50 (fifty-two to fifty) meaning that for each 50 men there are 52 woman. You can simplify this ratio and divide both terms by a common divisor and get a ratio of 26:25, which is equivalent.

Think of a bowl filled with balls. There are 11 balls inside it, 4 are red and 7 blue. What's the red:blue ratio? Just 4:7. What's the blue:red ratio? It'll be 7:4. Now, what's the blue:total ratio? It's the ratio that relates blue balls to the total amount of balls, so we must say it's 7:11, because for each eleven balls there are seven that are ping-pongs. In the same way, the red:total ratio would be 4:11.

We might transform a ratio into a quotient. For instance, a 1:2 ratio of notebooks to pencils may be expressed as1/2 meaning that the quantity of notebooks is 1/2 of the quantity of penciles. If you have six university students per professor, you would say the ratio is 6:1 and the quotient 6/1, that is, the quantity of students is 6/1 times the quantity of professors.

That's all good, but we need now a way to represent

*comparisons*between ratios. For example, if you want to know if there is a sort of relationship between weddings and rings, you probably want to compare the weddings:people ratio with the rings:people ratio. Let's suppose that there are 50 weddings per 1,000 inhabitants in some country in any given year, so the weddings:people ratio is 50:1,000. You also have the rings:people ratio: per each 500 people there are 25 rings. Then, the rings:people ratio is 25:500 or 50:1,000. Now you compare these two ratios by using this sign (::) between them, this way:50:1,000::25:500

And this expression states that the two ratios (weddings to people and rings to people) are the same. The two numbers in the extremes are called...

*extremes*, and the two in the middle are called*means*. If we simplify these rates, we get 1:20::1:20. This is read 'weddings are to people as rings are to people' or 'there are as many weddings per person as rings per person,' because there is 1 ring and 1 wedding per each 20 people. Indeed, you see that the weddings:rings ratio is 1:1, so that per each ring sold there was one wedding.Ratios can sometimes concatenate several terms. See these boxes:

Here, the blue:red:total ratio is 1:2:6 because there is 1 blue box per each 2 red boxes and there are 2 red boxes per each 6 boxes. See this three-terms ratios as two two-terms ratios merged into one. In the weddings example the marriages:people:rings ratio was 1:20:1.

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