# Upper Tail and Lower Tail: Definition

Statistics Definitions > Upper Tail and Lower Tail

## What is a “Tail”?

The “tails” of a distribution are, just like the name suggests, the appendages on the side of a distribution. Although it can apply to a set of data, it makes more sense if that data is graphed, because the tails become easily visible. For example, the following image shows the tails of a normal distribution:

Two tails of a normal distribution, highlighted in yellow.

The tail on the left is (perhaps not surprisingly) called a left-tail; The one on the right is a right-tail. A distribution doesn’t have to have both: it can have only one tail on one side.

## Upper Tail and Lower Tail

Although it’s more common to refer to the tails as being on the “left” or “right”, this can pose problems if you aren’t looking at a graph. In other words, if you’re dealing with a set of data, it won’t be very clear what data should go on the left or right of a graph. The alternate name for right and left tails, which addresses this issue, is upper tail and lower tail.

## Lower Tail (Left Tail)

The lower tail contains the lower values in a distribution. If you graph any distribution on a Cartesian plane, the lowest set of number will always appear on the left, because the lowest values on a number line are to the left. So, “lower tail” means the same thing as “left tail”.

## Upper Tail (Right Tail)

Similarly, the upper tail contains the upper values in a distribution. If you graph any distribution on a Cartesian plane, the highest numbers will always appear on the right, because the highest values on a number line are to the right. So, “upper tail” means the same thing as “right tail”.

One tailed test or two?

Heavy and light-tailed distributions.

Long tail distributions.

Fat tailed distributions.

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Statistical concepts explained visually - Includes many concepts such as sample size, hypothesis tests, or logistic regression, explained by Stephanie Glen, founder of StatisticsHowTo.