> For the complete documentation index, see [llms.txt](https://mey.istad.co/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mey.istad.co/statistical-techniques-in-business-and-economics/chapter-1-what-is-statistics/1.4-levels-of-meaurement.md).

# 1.4 Levels of Meaurement

Data can be classified according to levels of measurement

The level of measurement of the data dictates the calculations that can be done to summarize and present the data. It will also determine the <mark style="color:blue;">**statistical tests**</mark> that should be performed.

<mark style="color:purple;">**Four Levels of Measurement**</mark>

<table data-card-size="large" data-view="cards"><thead><tr><th></th><th></th><th></th></tr></thead><tbody><tr><td></td><td><mark style="color:green;"><strong>Nominal Level</strong></mark> </td><td>Data that is classified into categories and cannot be arranged in any particular order. <strong>Examples:</strong> eye color, gender</td></tr><tr><td></td><td><mark style="color:green;"><strong>Interval Level</strong></mark></td><td>Similar to Ordinal Level, with the additional property that meaningful amount of differences between data value can determined. <strong>Example</strong>: Temperature on the Fahrenheit scale.</td></tr><tr><td><mark style="color:green;"><strong>Ordinal Level</strong></mark></td><td>data arranged in some order, but the differences between data values cannot be determined or are meaningless. <strong>Example</strong>: During a taste test of 3 soft drinks, Sting was ranked number 1, Sprite number 2, Seven-up number 3</td><td></td></tr><tr><td><mark style="color:green;"><strong>Ratio Level</strong></mark></td><td><p>The interval level with an inherent zero starting point.  Differences and ratios are meaningful for this level of measurement.  </p><p><strong>EXAMPLES</strong>: Monthly income of surgeons, or distance traveled by manufacturer’s representatives per month.</p></td><td></td></tr></tbody></table>

<figure><img src="https://1664307983-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2Fm4ft0AbtTKwMPEcUcdTy%2Fuploads%2FSX3cHyq9N7JYz9xD6Y77%2FScreenshot%202023-11-11%20at%2016.36.46.png?alt=media&amp;token=cab11cc0-e815-4ed5-a20b-6632164125c0" alt=""><figcaption><p>Summary of the Characteristics for Levels of Measurement</p></figcaption></figure>

**Exercise**

1. What is the level of measurement for each of the following variables?

   a. Student IQ ratings.

   b. Distance students travel to class.

   c. The jersey numbers of a sorority soccer team.

   d. A classification of students by state of birth.

   e. A summary of students by academic class—that is, freshman, sophomore, junior, and

   senior.

   f. Number of hours students study per week.
2. What is the level of measurement for these items related to the newspaper business?&#x20;

   a. The number of papers sold each Sunday during 2011.\
   b. The departments, such as editorial, advertising, sports, etc.\
   c. A summary of the number of papers sold by county.

   d. The number of years with the paper for each employee.
3. For each of the following, determine whether the group is a sample or a population.

   a. The participants in a study of a new cholesterol drug.\
   b. The drivers who received a speeding ticket in Kansas City last month.&#x20;

   c. Those on welfare in Cook County (Chicago), Illinois.\
   d. The 30 stocks reported as a part of the Dow Jones Industrial Average.

<mark style="color:red;">**Answers:**</mark>&#x20;

1. a. Interval &#x20;

   b. Ratio

   c. Nominal

   d. Nominal

   e. Ordinal

   f. Ratio
2. a. Ratio

   b. Nominal

   c. Ratio

   d. Ratio
3. a. Sample

   b. Population

   c. Population

   d. Sample