Ordering & Ranking Data: Process & Example

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• 0:02 Using Data for…
• 0:35 Ranking Data
• 1:44 Types of Ranking
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Lesson Transcript
Instructor: Cathryn Jackson

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

Ordering and ranking data can often be more important than you might think. In addition to being an important part of competitions, ranking data can be another way of analyzing and evaluating research.

Using Data for Rankings in Competitions

Mickey is a local hot dog eating champion. At his last competition, he managed to eat 45 hot dogs and buns in 10 minutes. He's hoping to qualify for the national hot dog eating contest. For Mickey to go to nationals, he must place in the top three at his local contest. Take a look at the chart below to see how Mickey did compared to the other competitors. We need to figure out how Mickey placed and if he qualified for nationals by ordering and ranking this data.

Ranking Data

Ranking is the relationship between two mathematical values where each value can be less than, greater than, or equal to the second value. Mickey's placement in the hot dog eating tournament is dependent upon what type of ranking the competition officials will use. There are many types of official rankings, and often each tournament will have its own rules and regulations regarding ranking. For this lesson, we will look at standard competition ranking, ordinal ranking, and fractional ranking.

Standard competition ranking, or SCR, is a ranking system in which the mathematical values that are equal are given equal rank and the next, lesser value is given the next highest rank. Ordinal ranking is a system of ordering where each mathematical value is given a certain position in a sequence of numbers where no positions are equal. Fractional ranking is a system of ordering in which the mathematical values that are equal are given the mean of the ranking positions.

I know - there are a lot of definitions. Let's look at some examples to help you remember each one.

Types of Ranking

Let's start with standard competition ranking. To figure out Mickey's ranking, we first need to order the data greatest to least. Why greatest to least? In this competition, the more hot dogs you eat, the better. Therefore, the person with the greatest number of hot dogs is the best person. If we were looking at golf scores, where the person with the lowest score is the best, we would want to order our data from least to greatest.

So, our order is:

62, 53, 45, 45, 39, 34, 29.5, 28.5, 20

According to this order, the first place person ate 62 hot dogs, second place ate 53, but we have a problem when it comes to third place. There are two contestants that ate 45 hot dogs. According to standard competition ranking, the mathematical values that are equal are given equal rank and the next, lesser value is given the next highest rank. Therefore, both contestants would receive third place, and the contestant that ate 39 hot dogs would receive fifth place.

Notice that we skipped fourth place. For this particular ranking system, in this situation, fourth place does not exist because of the third place tie. It's kind of strange, I know. If the competition officials use standard competition ranking, then Mickey would qualify for the national competition.

Okay, let's move on to ordinal ranking. We already ordered our data, so let's take a look at it one more time:

62, 53, 45, 45, 39, 34, 29.5, 28.5, 20

According to the ordinal ranking system, each mathematical value is given a certain position in a sequence of numbers where no positions are equal. Therefore, the competition officials would have to come up with a way to break the tie, like a sudden death hot dog eating round.

Now for fractional ranking. Once again, let's have a last look at our data:

62, 53, 45, 45, 39, 34, 29.5, 28.5, 20

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