By utilizing Mid Rank, you are able to more easily make sense of the ranking of your ordered observations.

Overview: What is Mid Rank?

Mid Rank is a tied observation’s average rank. It is also known as average rank.

3 benefits of Mid Rank

There are some clear benefits of using Mid Rank:

1. Can be used to extend a test

You can allow for ties by patching the data and then utilizing the mid ranks instead of ranks.

2. One method of dealing with ties

A Mid Rank is one way of handling ties that are in a nonparametric test that is based on ranks.

3. Simplicity

The equation for finding the Mid Rank is fairly simple. It is dependent on the number of tied ranks (ℓ) and then, also, the number of items that are lower ranked (k). The easy formula below is used to find the Mid Rank:

Mid Rank = k + (ℓ + 1) / 2

For example, if there are 2 tied ranks and there are 4 items that are lower ranked, the equation would look like this:

Mid Rank = 4 + (2 + 1) / 2
= 4 + (3 / 2)
= 4 + 1.5

In this case, the Mid Rank would be 5.5

Why is Mid Rank important to understand?

Mid Rank is important to understand for the following reasons:


It is worth understanding because it is the most common way to handle ties in a nonparametric test.

It is the method recommended by Frank Wilcoxon

Frank Wilcoxon was a statistician who proposed both the Wilcoxon signed rank test and the rank-test sum. He recommended the Mid Rank test for dealing with ties in a nonparametric test.

Ease of use

It is worth knowing how to find Mid Rank as the equation for it is definitely the simplest method of sorting out ties.

An industry example of Mid Rank

A machine shop is testing how many units a selection of individual employees can produce in an hour. Once the observations are made, it is clear that ranking will be difficult as there are a number of ties. The Mid Rank method is used in order to make better sense of the rankings.

3 best practices when thinking about Mid Rank

Here are some practices to keep in mind when it comes to Mid Rank:

1. Assigning rank to an observation

The rank that is assigned to an observation should be the average of the potential ranks it would have it the ties were broken in all possible ways.

2. Performance gauging

Mid rank or average rank can sometimes be a better method of gauging overall performance than other methods.

3. Be wary of too many ties

Using Mid Rank on a set where there are too many ties might cause your ranking to become insignificant.

Frequently Asked Questions (FAQ) about Mid Rank

What does Mid Rank mean as far as status within a company or organization?

Mid Rank in a company refers to not having one of the most important positions, but still having some degree of authority.

What is the difference between mean rank and Mid Rank?

They are synonymous with one another.

Is median a rank statistic?

Yes, it is. You determine it by ranking observations and then finding the one that is at
[N + 1] / 2 in the order.

Mid Rank makes it simpler

When you have ordered observations and are doing a nonparametric test that is based on ranks, the Mid Rank method is a simple and helpful solution if you have ties.

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