Statistics Definitions > Ratios and Rates

**Contents (click to skip to that section):**

- Ratio Definition
- Rate Definition
- Which number goes first in a ratio?
- Other articles related to ratios and rates

## Ratio Definition

A ratio is a comparison of two numbers. It can be written in many ways. For example, the ratio of 5 to 9 can be expressed as:

- 5 to 9
- 5 out of 9
- 5:9
- 5/9

## Which number goes first in a ratio?

If you want to figure out which number comes first, make your problem into a “x out of y” statement. For example, let’s say you had 12 pieces of fruit, and 6 are apples. There are “6 apples out of 12 pieces of fruit”. Then just take out the excess words so it’s simply “6 out of 12.” Then you can rewrite that ratio in any form you like (e.g. 6/12 or 6:12). Just make sure to keep the numbers in the original order you had in your statement.

Another example: Out of 100 people, 76 like chocolate. This becomes “76 out of 100 people like chocolate” or 76/100.

## Rate Definition

A **rate **is a specific type of ratio that *usually *tells you how long it takes to do something. For example, a rate might be 100 miles / 10 hours. In simple English, that’s saying it takes 10 hours to travel 100 miles. We can reduce that fraction to a “per hour” statement (by using the greatest common factor or another similar method); simplifying, it becomes 10 miles per hour.

**In most cases**, a rate will have **time **in the denominator and is a measure of how long it takes to do something; the numerator will also have different units from the denominator, as in the above example. However, there are exceptions in common usage (like “tax rates” and “interest rates”), which have the same units and measure “something else” like interest charged per amount loaned.

## Other articles related to ratios and rates

*Base rate*: has a slightly different meaning depending on where you use it. In general, it’s the probability of some event happening.*Familywise error rate*: the probability of a coming to at least one false conclusion in a series of hypothesis tests .*Rate ratio*(epidemiology): compares the incidence of events happening at different times.*Rate parameter:*has several meanings; The most common use is to describe exponential distributions or event rates in Poisson processes.*Ratio Scale*: a scale of measurement where the difference between values is meaningful and zero is also meaningful.*False discovery rate (FDR)*: the expected proportion of type I errors.

## References

Doctor Peterson. Rate vs. Ratio. Article posted on The Math Forum. Retrieved June 2, 2018.

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