There are four measurement scales (or types of data): nominal, ordinal, interval and ratio.  These are simply ways to categorize different types of variables.  This topic is usually discussed in the context of academic teaching and less often in the “real world.”  If you are brushing up on this concept for a statistics test, thank a psychologist researcher named Stanley Stevens for coming up with these terms.  These four measurement scales (nominal, ordinal, interval, and ratio) are best understood with example, as you’ll see below.

Nominal
Let’s start with the easiest one to understand.  Nominal scales are used for labeling variables, without any quantitative value.  “Nominal” scales could simply be called “labels.”  Here are some examples, below.  Notice that all of these scales are mutually exclusive (no overlap) and none of them have any numerical significance.  A good way to remember all of this is that “nominal” sounds a lot like “name” and nominal scales are kind of like “names” or labels.

Examples of Nominal Scales

Note: a sub-type of nominal scale with only two categories (e.g. male/female) is called “dichotomous.”  If you are a student, you can use that to impress your teacher.

Continue reading about types of data and measurement scales: nominal, ordinal, interval, and ratio…

Ordinal
With ordinal scales, it is the order of the values is what’s important and significant, but the differences between each one is not really known.  Take a look at the example below.  In each case, we know that a #4 is better than a #3 or #2, but we don’t know–and cannot quantify–how much better it is.  For example, is the difference between “OK” and “Unhappy” the same as the difference between “Very Happy” and “Happy?”  We can’t say.

Ordinal scales are typically measures of non-numeric concepts like satisfaction, happiness, discomfort, etc.

“Ordinal” is easy to remember because is sounds like “order” and that’s the key to remember with “ordinal scales”–it is the order that matters, but that’s all you really get from these.

Advanced note: The best way to determine central tendency on a set of ordinal data is to use the mode or median; the mean cannot be defined from an ordinal set.

Example of Ordinal Scales

Interval
Interval scales are numeric scales in which we know not only the order, but also the exact differences between the values.  The classic example of an interval scale is Celsius temperature because the difference between each value is the same.  For example, the difference between 60 and 50 degrees is a measurable 10 degrees, as is the difference between 80 and 70 degrees.  Time is another good example of an interval scale in which the increments are known, consistent, and measurable.

Interval scales are nice because the realm of statistical analysis on these data sets opens up.  For example, central tendency can be measured by mode, median, or mean; standard deviation can also be calculated.

Like the others, you can remember the key points of an “interval scale” pretty easily.  “Interval” itself means “space in between,” which is the important thing to remember–interval scales not only tell us about order, but also about the value between each item.

Here’s the problem with interval scales: they don’t have a “true zero.”  For example, there is no such thing as “no temperature.”  Without a true zero, it is impossible to compute ratios.  With interval data, we can add and subtract, but cannot multiply or divide.  Confused?  Ok, consider this: 10 degrees + 10 degrees = 20 degrees.  No problem there.  20 degrees is not twice as hot as 10 degrees, however, because there is no such thing as “no temperature” when it comes to the Celsius scale.  I hope that makes sense.  Bottom line, interval scales are great, but we cannot calculate ratios, which brings us to our last measurement scale…

Example of Interval Scale

Ratio

Ratio scales are the ultimate nirvana when it comes to measurement scales because they tell us about the order, they tell us the exact value between units, AND they also have an absolute zero–which allows for a wide range of both descriptive and inferential statistics to be applied.  At the risk of repeating myself, everything above about interval data applies to ratio scales + ratio scales have a clear definition of zero.  Good examples of ratio variables include height and weight.

Ratio scales provide a wealth of possibilities when it comes to statistical analysis.  These variables can be meaningfully added, subtracted, multiplied, divided (ratios).  Central tendency can be measured by mode, median, or mean; measures of dispersion, such as standard deviation and coefficient of variation can also be calculated from ratio scales.

This Device Provides Two Examples of Ratio Scales (height and weight)

Summary
In summary, nominal variables are used to “name,” or label a series of values.  Ordinal scales provide good information about the order of choices, such as in a customer satisfaction survey.  Interval scales give us the order of values + the ability to quantify the difference between each one.  Finally, Ratio scales give us the ultimate–order, interval values, plus the ability to calculate ratios since a “true zero” can be defined.

summary of data types and scale measures

That’s it!  I hope this explanation is clear and that you know understand the four types of data measurement scales: nominal, ordinal, interval, and ratio!

## You may also like

• Time is in fact a ratio scale.
20 seconds is twice as long as 10 seconds. You can multiply and divide time. The absolute 0 doesn\’t have to be attainable for the scale to be ratio. To borrow from your example: there is no such thing as \”no height\”, yet you\’ve classified height as ratio.

March 13, 2013 at 10:36 am
• Thanks for the excellent comment, LJ. I have edited the article based on your comment. Time is a tricky one. This article from UC Davis explains how time, depending on how it is presented, can be categorized as any of these types of scales. http://psychology.ucdavis.edu/sommerb/sommerdemo/scaling/levels.htm

October 29, 2013 at 6:30 pm
• I have a better understanding of the four levels of measurement. You explain the information better than my textbook.

January 28, 2017 at 2:01 pm
• Thanks for this informative text. Now I became clearer between these four terms.

April 26, 2013 at 3:14 am
• Thanks for that brilliantly written info. Really helped clear all of my confusion regarding scales, especially the difference between interval and ratio. Thanks again.

June 16, 2013 at 11:10 pm
• Thanks this helped me a lot!

September 23, 2013 at 7:00 pm
• Thank you so so much. Im doing a BA in Psychotherapy and one of our modules is Psychology so we only touch on it in one class so Im not au fait at all. You have explained to me in 10 minutes what I could not understand from our lecturer in a 2 hour long lecture. Feel more confident about the exam for this module next Monday!

November 16, 2013 at 4:55 pm
• Thanks so much,since now i understand those scales especial to differentiate them.

December 6, 2013 at 11:29 pm
• Very formative article, thanks to author for such a great job!

February 24, 2014 at 6:10 pm
• Brilliant article though, however I had one doubt regarding oil prices in exact USD figure over a monthly period. On which scale should these values lie. Appreciate your inputs.

March 26, 2014 at 2:25 am
• That would be a ratio scale. \$0 is a meaningful number, and the intervals between values are equal (i.e. the difference between \$1 and \$2 is the same as the difference between \$99 and \$100). A clear indication of this fact is that you can easily multiply and divide monetary values. E.g. 1 barrel of oil costs \$100, then 2 barrels will cost 2X as much, or \$200.

December 4, 2015 at 7:48 pm
• Difficult things made really simple and easy to understand.

March 29, 2014 at 10:35 pm

April 7, 2014 at 7:24 pm
• Thank you very much, you are a good teacher.

April 17, 2014 at 5:41 am
• much appreciated author i got informed a lot in these scales

May 4, 2014 at 5:48 am
• Tnx a lot…..

May 23, 2014 at 11:58 am
• THANKS. I NOW HAVE A BETTER UNDERSTANDING BETWEEN THE FOUR MEASURES

June 22, 2014 at 6:17 am
• very easy to understand thank you 🙂

July 6, 2014 at 4:07 am
• Excellent & Simple explanation with examples for clarity.

September 7, 2014 at 5:32 am
• Excellent & Simple explanation.

September 7, 2014 at 5:33 am
• Excellent & Simple explanation

September 7, 2014 at 5:34 am
• very nice tnx

September 29, 2014 at 11:52 pm
• I am very impressed with your detailed and easy explanation.. wish u get reward for this 🙂

September 30, 2014 at 1:59 pm
• Thank you. I am very impressed with your boxing career.

May 11, 2016 at 3:27 am
• This information came in handy. thank you so much.

October 31, 2014 at 8:07 am
• well explained

November 20, 2014 at 4:30 am
• Celsius is not really a good example for a true zero, as people experience 0 degrees Celsius quite often. A better example would be 0 degrees Kelvin. Semantics, I know, but it\’s easier to understand if phrased in K.
Great explanations otherwise.

December 2, 2014 at 3:51 pm
• Thank you sir. it is very helpful me for broden my knowledge.

December 2, 2014 at 8:42 pm
• This explanations kinda help. I wish can get more verbal explanations.

December 6, 2014 at 3:36 am
• Your explanations were very explicit and illustrative. My knowledge has greatly improved on the 4 levels of measurements

January 6, 2015 at 3:50 pm
• I truly enjoyed reading thru this paper. Simple language, simple and to the point explanations. I appreciate you for your effort to share this with persons like me, finding hard to comprehend statistics. Thanks a lot

January 18, 2015 at 1:45 pm
• Thanks … It helped me a lot to understand the measurement scales.

January 21, 2015 at 12:49 am
• Thanks alot

February 1, 2015 at 5:48 am
• Nice work…helped me in my assingment

February 4, 2015 at 11:21 am
• quiz of basic statistics
1)Temperature measuring on a kelvin scale.
2)military ranks
3)HIV/AIDS status
4)Coli form bacteria counts in drinking water supplies

February 7, 2015 at 4:39 am
• I am doing a make up research in clinic no show rates. Taking the amount of patients scheduled on a given day, and the amount of patients that actually show. What type is this?

February 9, 2015 at 10:09 pm
• This article has helped me understand what I am studying, different types of vocational testing. I needed to understand the basic concept. Very helpful. Thank you

February 10, 2015 at 10:45 pm
• great article and very helpfull

February 13, 2015 at 2:57 am
• Very precise and clear. Thank you

February 20, 2015 at 2:31 am
• your explanations were simple deep,illustrative,awesome thank you keep it up

March 29, 2015 at 9:48 am
• it was more informative to me and ur way of examples in each types scale was outstanding and easily to understabke thank you so much……..

April 10, 2015 at 5:44 am
• give this man a bells

April 10, 2015 at 10:46 am
• Being a Quality Engineer. Its very important to know all the scales. This article was very informative..

Thanks

April 12, 2015 at 7:17 am
• Clear and useful, thanks a lot.

April 19, 2015 at 1:04 pm
• Thank You. Learnt lot in a flash, summary was brilliant.

April 23, 2015 at 5:56 am
• Excellent explanation for scales

April 24, 2015 at 1:13 am
• Thanks alot for the detailed explanation of measurements of scale, keep it up.

April 25, 2015 at 4:36 am
• That was soo simple and informative…thumbs up

May 9, 2015 at 5:10 am
• I just recently signed on for a Msc in health education..and statistics is one of the modules…This is helping me a lot. Wouldnt mind more though!

May 11, 2015 at 4:00 am
• Many thanks for the explanation. It helped me solve my assignment in an educational course and has also enlightened me more.

May 19, 2015 at 1:13 pm
• great explanation!! short and sweet, straight to the point. Awesome thanks!!

May 25, 2015 at 4:34 pm
• Invaluable! I found myself a gold chest. I wish I found this website so much earlier, not the day before the due like this.I will visit the website often in the future!

June 10, 2015 at 8:16 am
• I think 0 is the same as 24 so we can\’t count time as ratio data even on the 24 hour clock unless you remove 24 from the data set and end at 23.

June 14, 2015 at 2:41 pm
• Thank you so much sir and ma\’am, this serves as my nirvana about scale of measurement. 🙂

July 29, 2015 at 11:13 am
• So, Nominal & ordinal are qualitative and interval & ratio are quantitative variable. These are scale of data measurement. But ordinal can be both qualitative and quantitative. Can it?

July 31, 2015 at 4:24 pm
• thanks this is wonderful work.#kevin, but how would you classify the teachers job groups in a staff?

September 29, 2015 at 12:51 am
• Thank you for the great job. I like the bit on how to remember, nominal is like name, ordinal is like order. That was creative. Keep it up!

August 3, 2015 at 9:51 am
• Brilliant article! A very QQ: why do you classify temperature as being interval. I agree there if nothing called \\”no temperature\\” , but isn\\’t 20°c twice as hot as 10°c or am I wrong? Please clarify. Also, another ex of ratio scales would be very very helpful.

August 8, 2015 at 9:50 am
• Mucho gracias, yo soy incanatado en meteriale, chao

August 13, 2015 at 8:38 am
• Thanks for such clear and understandable explanation

August 23, 2015 at 7:16 am
• What of binary scale?

September 16, 2015 at 11:16 am
• Wow! Those examples simply nailed the explanations inside my memory. Thanks a lot.

September 18, 2015 at 12:19 am
• To make things clearer, pls don’t confuse ‘true zero’ to mean that zero is a valid number on a scale.for example, the height of an individual being 0cm. ‘true zero’ means there are no negative values for the scale being considered, as in the height of a person being -100cm which is invalid. The Celsius scale is said to have ‘no true value’ because negative values are actually valid for the Celsius temperature scale. For instance , the temperature of ice could be -4 degrees Celsius. So weight and height have a true zero.

September 19, 2015 at 5:16 pm
• The ‘no true value’ should be ‘no true zero’ , sorry

September 19, 2015 at 5:49 pm
• Good clarification. thanks!

October 23, 2015 at 9:18 am
• Thank you so much

September 26, 2015 at 7:48 am
• Excellent!!

September 27, 2015 at 5:49 pm
• The clearest information ever! Thank you so much 🙂

September 29, 2015 at 10:01 pm
• great job.its amazing.
simplify and brief

October 14, 2015 at 5:28 pm
• what about these? Is the following nominal, ordinal, interval, or ratio scale?
A score of 90 out of a 100 on a test
A salary of \$32.000

October 20, 2015 at 4:11 pm
• Ratio

October 23, 2015 at 9:17 am
• thanks for such a clear explanation

November 15, 2015 at 4:06 pm
• You cannot multiply or divide with scores or \$ eg \$32 x \$32, 90% / 70% – no mathematical or statistical meaning on these. Hence the example should be Interval.

April 18, 2016 at 3:47 am
• Quantity of sand minned daily e.g 1-5, 6-10 trucks per day. What measurement scale is that? How can it be analyzed?

November 30, 2015 at 3:05 am
• so much lucky explanation, I m 2nd year of university and I have been confused by the lecture .
but now i have got the point and impressing great thank for your helping well ,encouraging you to keep up this helping.

November 30, 2015 at 9:48 am
• Brilliant explanation of an otherwise mixed up knowledge of measurement scales in some textbooks. Thanks a Lot.

December 7, 2015 at 3:22 am
• Thanks very much , it help me very much I appreciate your procedure to displaying the information.

January 1, 2016 at 1:54 pm
• Thank you very much. Very helpful to clear my mind on measurement scales.

January 12, 2016 at 2:27 am
• thanks thanks thanks.
i would also like to know in situations where interval or ordinal data is taken as nominal data.

January 25, 2016 at 9:41 am
• thanks for providing such a information about better understanding of scales for measurement.
its really helpful and clear out the confusions between these scales.
provided examples really appreciable.

February 2, 2016 at 1:11 am
• Yes I agree this is the best explaination I came across so far. Crystal clear and concise.

February 7, 2016 at 4:50 am
• 5. Researchers at Princess Margaret Hospital measure patients’ pain using the Pain Survey where 0 = no pain and 10 = excruciating pain. What level of measurement is their survey? What measure of central tendency (mean, median, mode) can they report?

Can anyone help me with this question here, i\\’m a bit stuck

February 16, 2016 at 8:23 pm
• Ordinal. The best way to determine central tendency on a set of ordinal data is to use the mode or median; the mean cannot be defined from an ordinal set.

March 8, 2016 at 4:21 pm
• The best explanation I ever had. You are super! I wish you could be my statistic professor.

February 28, 2016 at 8:40 pm
• This was exactly what I needed to read. This was simple and clearly differentiated the terms quite nicely. I’m ready for my text today.

March 8, 2016 at 9:30 am
• Thank you very much, I got more detail about measurment scale . I am preparing Master in Development Studies

March 13, 2016 at 10:41 pm
• For the question, \\\”How many courses have you taken in this year?\\\” is nominal or ratio scale?

April 2, 2016 at 1:07 am
• Sounds like a ratio scale to me. Absolute zero, known order and values.

May 11, 2016 at 3:37 am
• I am research scholar,i need standred scale for labour welfare measures.

April 11, 2016 at 2:01 am
• Hi

I am conducting a study with four variables and in one of them, the scores are as decimals (e.g. 4.3, 5, 3.2…\”) all four variables were measured with Likert scale questionnaires, would the data still be ordinal?

April 16, 2016 at 10:05 am
• Good article. On nominal/categorical data, I think you can calculate/determine the mode. Mode is the most common value in a dataset e.g. In an experiment, note what colour of shoes each participant is wearing on a particular day. Results Yellow = 5, Blue = 13 Read = 7, black = 27. Hence the mode is black since its the most occurring colour of shoes. Therefore amend the table such that you have a row for Mode, and another one for Median. Then have a tick under Ordinal, see below:

Provide Nominal Ordinal Interval Ratio
Mode Yes Yes Yes Yes
Median Yes Yes Yes

April 18, 2016 at 3:40 am
• Good comment and point. I agree and will update the table. Thanks!

May 11, 2016 at 3:32 am
• Great explanation

April 21, 2016 at 6:26 am
• Thank you, well explained

April 23, 2016 at 11:08 pm
• Thank you so much!

May 13, 2016 at 10:21 am
• Thanks Market Reaserch Guy

May 15, 2016 at 8:30 pm
• This is a very helpful article.God bless the author

May 23, 2016 at 12:49 pm
• thank you for the better understanding

June 8, 2016 at 9:13 pm
• Very well written article – concepts articulated in a simple manner. Thank You.

June 16, 2016 at 9:23 am
• Thanks for this lovely article on measurement.

July 7, 2016 at 12:08 am
• Great presentation and definitions. Thank you

July 10, 2016 at 9:02 pm
• Too good an explanation. This is by far the best article i read on scales. Crisp, candid, clear and concise. Thanks a lot.

July 12, 2016 at 2:12 pm
• Wow this is really good now I understand

July 14, 2016 at 12:03 am
• As a physicist being forced to do pedagogical research I both appreciate this article and the image at the top. Cheers!

July 29, 2016 at 10:45 am
• This is a wonderful and simple explanation – I wonder if you have considered making a video presentation and linking it to TeacherTube, Youtube, Vimeo, or some similar format? As many have already expressed, yours is perhaps one of the simplest and straightforward explanations for an otherwise complex topic.
– Just a thought

Thank you very much!

August 12, 2016 at 12:27 pm
• Thanks. Yes, I intend to add a video and update this post a bit once I have some time.

October 6, 2016 at 11:19 pm
• what is the level of measurement for bank account balance and why?

August 12, 2016 at 11:50 pm
• Ratio. One can have \$0 balance.

October 6, 2016 at 11:18 pm
• Thanks for this article 🙂 u help me a lot :*

August 17, 2016 at 3:52 am
• thank you so much for your help

August 19, 2016 at 9:53 am
• The score of 57.11 out of 70?

August 27, 2016 at 8:56 pm
• What scale of measurement is used for the number of pizzas consumed during the second week/ and the number of days people got sick

September 18, 2016 at 12:28 am
• Sounds like a ratio scale to me.

October 6, 2016 at 11:12 pm
• In which scale does nationality falls?

September 27, 2016 at 4:10 am
• Nominal

October 6, 2016 at 11:08 pm
• Thank you.
The response has been quite helpful

September 28, 2016 at 1:32 am
• Thanks is so explanatory,even with the examples.

October 4, 2016 at 6:53 pm
• This is really helpful and clear!, Thanks so much!

October 8, 2016 at 12:40 pm
• thanks, for great article.
what about Zip Code and salary

October 9, 2016 at 5:57 am
• Temperature is *ratio* when we use the unit Kelvin.

October 19, 2016 at 3:42 pm
• also want to know about difference value and absolute value. thanks

October 28, 2016 at 10:38 am
• There is such a thing as no temperature. It is called absolute zero. It is represented on the Kelvin and Rankine scales, both of which have zero at absolute and are ratio data scales. The Celsius and Fahrenheit scales have zero placed arbitrarily (absolute zero exists on those scales, but is not nominally zero in either of them), and so those scales are interval but not ratio.

November 21, 2016 at 12:08 pm
• You have done a very good job. Please keep it up.

November 22, 2016 at 9:17 pm
• I am currently doing my BA in hospitality management. My research is on peoples perceptions of Self-service technology in the industry and if it is taking the hospitality element away from the experience. I am trying to work out which measurement of scale would be best used. I am using interviews to gather data.

Any help would be appreciated 🙂

November 25, 2016 at 11:00 am
• Wow, what a great article. I have learnt in a few minutes what has been taught to me over the last few months (not so clearly). Really easy to read and has helped a lot. Much appreciated.

November 28, 2016 at 4:18 pm
• Thank you so much.

December 8, 2016 at 3:31 am
• Excellent explanations with examples. Thank you so much.

December 16, 2016 at 8:48 am
• I understand the definition of Interval but am having trouble applying it. Your explanation has helped some but I am still trying to wrap my brain around whether something has an absolute zero or not. What would you say the following are classified as?
Per capita income
Profit/loss in dollars

January 25, 2017 at 10:30 pm
• I have a better understanding on the four levels of measurement. You explain the meanings better than my textbook .

January 28, 2017 at 2:05 pm
• If the interval measure cannot be divided, then why in the chart does it say that a “mean” can be produced from it?

February 10, 2017 at 4:21 pm
• Very good and simple explanation

March 7, 2017 at 8:32 am
• thank you !!!!!!!!!!!

March 23, 2017 at 1:28 am
• thank you !

March 23, 2017 at 4:55 am
• Very useful – well explained.
Thank you 🙂

March 30, 2017 at 5:20 am
• Very well writeen. However, I have seek the following clarification from you.
What is your favourite sports? Answer to this will form a nominal data or ordinal data?
What kind of music do you like? It is an open ended question. Answer to this may result in more than one category like Western music, Indian music, folk music etc. How do you categorise this data? Nominal or Ordinal?

April 2, 2017 at 11:02 pm
• well explained… and easy to understand..

April 12, 2017 at 8:02 am
• great learning for me.
nice piece of knowledge.

April 19, 2017 at 10:11 pm
• Simple explaination

April 23, 2017 at 6:18 am
• Very useful explanation thanks a lot

April 25, 2017 at 8:34 am
• Qty of mined sand daily would be ratio. 1st, there\’s a true and meaningful zero, ie, it\’s conceivable that there is a day when you get absolutely NO sand. 2nd, you can divide or multiply to get ratio of sands mined on different days, ie, 10 trucks on Monday is 2x the 5 trucks on Wed.

April 26, 2017 at 5:57 pm
• This is a great work ! Thanks Sir

April 28, 2017 at 4:16 am
Thank U the writer….

May 1, 2017 at 12:39 pm
• Excellent discussion. Very informative indeed!

May 2, 2017 at 2:51 am
• Thank you, helped me with my UX studies! Greetings from Cape Town, South Africa.

May 20, 2017 at 10:42 am
• Thanks for elaboration.

May 30, 2017 at 11:30 pm
• thank you,it helped me a lot to understand

June 13, 2017 at 4:44 am