Levels of Measurement

Classify data into nominal, ordinal, interval, or ratio levels and identify which arithmetic operations are meaningful for each.

Opening

A temperature of 80°C and a score of 80 on a test both look like numbers, but one can be said to be 'four times' another and the other cannot. Why?

The idea

The ratio scale is the most informative level of measurement because it has a true zero, allowing ratios to be calculated.

Interval data's limitation

Interval level data can be used in calculations, but one type of comparison cannot be done. 80°C is not four times as hot as 20°C (nor is 80°F four times as hot as 20°F). There is no meaning to the ratio of 80 to 20 (or four to one).

Definition

ratio scale

A scale of measurement that, like the interval scale, has ordered values with meaningful differences, but also has a true zero point, so that ratios of values are meaningful.

A scale where zero means 'none of the thing', so you can say one value is twice another.

Worked example

Consider four exam scores: 80, 68, 20, and 92.

1
Order the scores from lowest to highest: 20, 68, 80, 92.
Ordering is possible because the scores are numbers with meaningful order.

2 more steps

Ratio scale data

Ratio scale data is like interval scale data, but it has a 0 point and ratios can be calculated. For example, four multiple choice statistics final exam scores are 80, 68, 20 and 92 (out of a possible 100 points). The exams are machine-graded.

Frequency distribution

Twenty students were asked how many hours they worked per day. Their responses, in hours, are listed below.

Definition

frequency

The number of times a value of the data occurs in a data set.

How often a specific value shows up in your data.

Table

Frequency table of hours worked per day by twenty students

Hours Worked	Frequency
2	3
3	5
4	3
5	6
6	2
7	1

How to read it

Each row shows one distinct value (hours worked) and how many students reported that value. For example, the row '5 | 6' means six students worked 5 hours.

The table lists the different data values in ascending order and their frequencies.

Recap

Say each point to yourself, then tap it to check.

Clear the page · $6.67/mo

Source

Barbara Illowsky and Susan Dean

Licensed under CC BY 4.0. This course is an adaptation, not the original work.

Access for free at openstax.org/details/books/introductory-statistics-2e