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Upper Tail and Lower Tail: Definition

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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:

one tailed test or two

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”.


References

Gonick, L. (1993). The Cartoon Guide to Statistics. HarperPerennial.
Lindstrom, D. (2010). Schaum’s Easy Outline of Statistics, Second Edition (Schaum’s Easy Outlines) 2nd Edition. McGraw-Hill Education
Vogt, W.P. (2005). Dictionary of Statistics & Methodology: A Nontechnical Guide for the Social Sciences. SAGE.

See also:
Left or Right tailed? How to tell in easy steps.
One tailed test or two?
Heavy and light-tailed distributions.
Long tail distributions.
Fat tailed distributions.

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Stephanie Glen. "Upper Tail and Lower Tail: Definition" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/upper-tail-and-lower-tail/
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