# Simple Mean/Average

I have results from a likert scale 1 - strongly disagree-5 - strongly agree. I also had a N/A and a Not Sure category. How do I calculate the average response?

I am thinking to not include the n/a's and not sure's in my calculation because we only want to be evaluated by people who know about my company.

• There are several questions on the site that hit on various aspects of your question. In addition to @PeterFlom's answer below (+1), I would suggest you read through several of the highest voted threads under the likert tag (list). – gung - Reinstate Monica May 28 '13 at 20:33
• stats.stackexchange.com/questions/31598/… contains discussion of the main disagreement, between those who say that you should not use means, as a matter of principle, and those who do this and assert that it works well in practice (consider grade-point averages in universities). One simple practical point is that the median must necessarily be one of the original values and may well give the same answer for several different questions. In practice, I would often take the mean and the median and then compare carefully, looking at graphs too. – Nick Cox May 29 '13 at 5:38

With a single Likert question, you can't really take the mean at all. If your interest is purely descriptive, just give a table or a chart of the number of people who gave each answer. Or, if you want, you could give the median, but that probably won't be as useful.

The reason you can't take the mean is because you don't know if the gaps between categories are equal.

I agree about excluding the NA and NS responses in your case.

EDIT - Example of calculating the median. Suppose your data are:

1 - 100
2 - 150
3 - 300
4 - 250
5 - 200


total = 1000. The median is, of course, the number that splits the data in half. One method would be to just note that that 250 cases are 1 or 2, while 550 are 1, 2, or 3 so the median is 3. This treats the numbers as strictly ordinal.

Another method is to assume that the numbers are somehow representations of an underlying continuous variable and say that the 500th case occurs 200/250 = .8 of the way through level 3, and say the median is 3.8. I don't like this method. It's better for binned data, in my view.

• thank you! How can I calculate the median? My manager wants one number that is the average response to the question. We are being evaluated on this one number each year. – megan May 28 '13 at 20:32
• I will update my answer to respond. – Peter Flom May 28 '13 at 21:54
• "The reason you can't take the mean is because you don't know if the gaps between categories are equal." --- however, if you regard it as acceptable to add the individual items together, you have already assumed this. If you can add Likert items, you can calculate means of said items. If you regard calculating means as unacceptable, you have no basis on which to add items. – Glen_b May 29 '13 at 0:15
• It's strange, but people see to accept adding Likert variables but not taking the mean of individual ones. In part, I think this comes from the fact that they aren't really ordinal or interval, but in between. – Peter Flom May 29 '13 at 9:57

We all might benefit from distinguishing between "Likert" scales and "Likert-like" scales, or "Likert-appearing" scales. They really are not quite the same. Here's a brief background that I hope will help.

The specific procedures for constructing scales were developed before the 1960s so they are not "new" or "modern" topics to teach in college nowadays. However, the psychometric procedures of scale development always included quite a number of specific steps which, collectively, ensured that the final scales were truly interval scales at the least. (Some practitioners argued that they might even produce ratio measurement scales.)

I suggest you find a couple old references on scale construction and development if you really want to learn why any particular scale is interval instead of ordinal or nominal. I think Likert developed his scale around 1950, and Thurstone (equally-appearing intervals) developed his in the 1930s or thereabouts. Guttman developed his scalogram analysis procedures around the same general time period.

None of the final "short-cut" scaling products (e.g., Likert-like or Thurstone-like) by themselves can convey the logic or validity that a full set of scaling procedures build into those scales. By the end of the 1960s, however, most scale construction procedures were discontinued. By then, sufficient research had demonstrated that "Likert-like" shortcuts could produce results equivalent to the full scale development process.

In the late 1960s or early 1970s, the Journal of Applied Psychology devoted a full issue to this very topic. Findings showed a very strong consensus among psychologists and psychometricians that the considerable time and expense of scale construction could be safely eliminated when scales were written by people with sufficient psychometric education and training.

From time to time, the final condition of "sufficient psychometric" background has perhaps been taken a little too much for granted. Without a firm psychometric foundation, some simple-but-vital qualities that help to ensure scale validity can easily be missed during development. Just like anything else that can become complex, people who lack a sufficient background might very well produce invalid scales through a simple lack of knowledge.

People who use scale products as part of their professional careers should certainly have at least a moderate level of psychometrics in their educational preparation. If a college fails to recognize that connection then that college is producing graduates were don't understand an important part of their professional practice (an opinion).

• +1 Welcome to our site! Thank you for an interesting and helpful answer. It's especially nice to learn some of the historical background. – whuber Mar 18 '17 at 19:08