# Average value from ranges in a survey

I have a questionnaire where some of the questions concern ranges, the answer alternatives are:

• 0
• 1 - 15
• 16 - 30
• 31 - 45
• 46 - 60
• 60+

(the numbers are minutes per week, not that it matters)

If I would like to present the result as an average number, how would I do this?

My thinking right now is just to take the average in the range (1 - 15 => 7), times how often it was selected. Then sum it for all alternatives and divide by the total number of answers. Not sure how to handle the 60+ value yet though.

But it seems to simplistic and since it looks like a problem that must occur quite often, there might be some better method.

Edit: A little background: The survey is regarding sources of inefficiencies in the workplace, like issues with slow servers, slow computers, using the wrong programs, etc. There are questions for several areas, and for each area the user will answer an estimate of how much time is lost, in minutes per week, in that particular area. I was looking for an average since I thought it would be an effective way to present the results; "On average, a developer loses X minutes per week due to an inefficient workplace. This means we could save Y money if we....". There is no need for it to be precise, it will just be used as an indicator and give some incentive for change.

• Can you tell us more about why you want an average? Like Max pointed out, there are some concerns with that approach. But, depending on how you want to use the data, those concerns may be acceptable. Jan 17, 2012 at 23:56
• Also, do you have any other data that would tell you what the "expected" distribution looks like, and what the 60+ looks like? For example, much is known about the typical distribution of ages in the US, and categorical data can therefore be intelligently interpolated. Jan 17, 2012 at 23:58
• @Jonathan Edited to add some background. Jan 18, 2012 at 8:31
• I suggest that you report: more than 50 % spend at least 30 min where 10 % spent over 60 min. You should be able to do some calculations based on that assumption. If you do an estimate where you take the average you risk actually damaging your case and they will probably not listen to your proposal Jan 18, 2012 at 18:02
• Do you have any other info on these time wasters? If I was trying to rank these sources of inefficiency and advocate for change, I would go for what's causing the most pain. Not all time lost is the same quality. You might hear from engineers that some source of time loss is very infrequent, but always comes up when they are trying to repair broken servers, for example. Or, 60 minutes lost per week might not be so painful if it comes all at once because it can be planned for, or it might be more painful because it interferes with a release. Jan 18, 2012 at 22:22

I think that using a pseudo-number for each group is a really bad idea. Let's say your measuring minutes on the internet per day it is probable that people who sit only 1-15 min. actually just sit 1 minute on average since they only do a fast check on something insignificant. The assumption that the distribution is even seems daring to me. As you also point out the fact that 60+ doesn't have an upper bound the idea of getting a proper average.

In general categorizing a continuous variable is a bad idea, the error is not smaller because you have categories, someone that sits 15 minutes per day will have a larger chance of getting misclassified. If you have to categorize you should do it after the collecting of data.

My suggestion is that you try to just do a bar graph showing the mode of the data or even more simple a frequency table. You could analyze your data using a multinomial logit or ordered logit (since your data has an order) if it's your outcome variable.