# Nominal, Ordinal, Interval & Ratio Measurements: Definition & Examples

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• 0:05 Understanding Data
• 0:50 Nominal and Ordinal Data
• 2:41 Interval and Ratio…
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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.

Different types of data can be grouped and measured in different ways. In this lesson, you will learn about nominal, ordinal, interval, and ratio measurements.

## Understanding Data

Chloe is working on a project for her agriculture class. She is growing and classifying different types of flowers. So far, she has collected data on the different types of flowers, the color of the flowers, the height of the flowers, and the number of petals on each flower. In order to analyze all of the data that Chloe has collected, she will need to understand the different types of data.

First, data is just information that is collected for analysis. Data is generally used to either disprove or prove a hypothesis. Data can be grouped into two different types of information: categorical and quantitative. In this lesson, we will be talking about two types of categorical data: nominal and ordinal. We will also be talking about two other types of measuring data: interval and ratio measurements.

## Nominal and Ordinal Data

First Chloe collects information about the different types of flowers she's growing, and the colors of each. She counts 4 roses, 6 daisies, 3 sunflowers, and 4 lilies. The colors of the flowers are 3 red, 4 yellow, and 10 white. She decides to assign a code to each type and color of flower to keep track of this information in her records.

According to this table, a red rose would have the numerical code 15, with the first number representing the flower type and the second number representing the color. As far as the data is concerned, the number 15 does not need to be added, subtracted, multiplied, divided, or ordered in any way. It does not have a value of 15; it is simply a code to indicate a red rose. This is an example of nominal data, or categorical data that assigns numerical values as an attribute to an object, animal, person or any other non-number. This is similar to the numbers that are given to horses during a race. The numbers themselves have no value, they simply identify the horses.

Next, Chloe has entered her roses into a local gardening competition. She had one rose get 4th place, one got 7th place, and one got 2nd place. These rankings are an example of ordinal data, which is data that can be ordered and ranked, but not measured, such as levels of achievement, prizes, rankings, and placements. Similar to nominal data, ordinal data cannot be multiplied, divided, added, or subtracted. However, the difference between ordinal data and nominal data is that the data can be ordered. Because ordinal data has to do with placement and rankings, you can order the data in descending or ascending order. When remembering ordinal data, think ordinal=order.

## Interval and Ratio Measurements

Chloe has entered another rose competition. This time, her flowers have to fit in certain categories. As she is filling out the paperwork, she notices some unusual questions. Take a look:

The second question represents a form of measurement called interval measurement, which is data that is grouped in evenly distributed values and measured based on the group to which that variable is attributed. In other words, interval data is measured in groups, rather than individually. For example, Chloe can measure the distance between each leaf and come up with .7. However, if the competition managers are trying to collect and group data in a more manageable way, then they will ask her to circle the option that is .5-1 inch. If you are collecting this information, you can really get a good visual representation by using a bar graph to display the data like this:

The next question asks about how many petals there are on Chloe's flower. You can take data like this and make a comparison. For example, what if the competition managers wanted to know how many flower petals there are in comparison to the leaves? They can learn this by using another form of measurement called a ratio, which is a mathematical comparison between two numbers. This can be represented with a colon; however, we can take a ratio and manipulate it to gather more information about our data. For example, if Chloe has 6 leaves and 12 petals, then we could write that ratio like this: 6:12. We can also easily see from this that there are twice as many petals as there are leaves. However, how would you find this comparative information if the ratio was more complicated? Let's take another look at Chloe's survey.

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