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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.

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  • $\begingroup$ 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. $\endgroup$ – Jonathan Jan 17 '12 at 23:56
  • $\begingroup$ 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. $\endgroup$ – Jonathan Jan 17 '12 at 23:58
  • $\begingroup$ @Jonathan Edited to add some background. $\endgroup$ – Fredrik Jan 18 '12 at 8:31
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    $\begingroup$ 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 $\endgroup$ – Max Gordon Jan 18 '12 at 18:02
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    $\begingroup$ 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. $\endgroup$ – Jonathan Jan 18 '12 at 22:22
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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.

Edit after comments

Reporting the data as a cumulative data also makes sense: 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 that will give you a minimum estimate.

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    $\begingroup$ +1 for the bar chart and frequency table. I would also add cumulated frequencies to the table. They will tell how many people have spent less than 30 minutes, less than 45 minutes, ... $\endgroup$ – user5644 Jan 17 '12 at 14:26
  • $\begingroup$ While I agree with you in principle, if this is one of many data points being shared in a summary, this approach may be overkill... $\endgroup$ – Jonathan Jan 17 '12 at 23:55
  • $\begingroup$ Ill be going with the suggestion in the comment to the question about using percentage rather than a average value, but ill mark this as the answer. $\endgroup$ – Fredrik Jan 19 '12 at 12:42
  • $\begingroup$ Thanks, good luck with your presentation. I guess if you could show that the time interval has a normal distribution you could do an average but if your trying to convince someone I would think that a more giving a careful estimate of the saved time gives much more credibility to your presentation. You also spark their imagination by allowing the interpretation that this is the "bare minimum" that they'll save :-) I'll edit my answer to contain the comments $\endgroup$ – Max Gordon Jan 19 '12 at 13:41

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