Mean Vs. median when dealing with ordinal data

Update 1: I’d be great if someone with actual mathematical knowledge could if and whythey disagree..!

Update 2: Seems the discussion has gone to Facebook - unfortunately the good parts are in Danish, but you could give it a shot, if you want.. See it here..

Update 3: It would seem my limited knowledge of math has caught up with me.. Apparently, in the case I proposed, I wasn’t using ordinal, but interval data, as the 5 points are arguably positioned with the same spacing (at least that’s what I based my argument on).. So, acknowledging that, my point would be this; why would you ever use ordinal data to measure user satisfaction with a feature of your product? Special thanks to Jacob Packert for teaching me the difference between ordinal and interval! Don’t forget to vote for him, when he runs for President of Planet Earth some day..!

As some of you might know, I’ve gone back to school.. I have yet to learn much there, but it’s nice being at it again, and I’m sure it will pick up soon.. In 8 days of classes I hadn’t exactly been challenged, until yesterday afternoon, when David Kocmick talked to us about surveying clients in order to analyze the customer->product relation. I’d say I know my fair share about surveying - after all, I did spend more than a year at Synovate, where I helped organize a ton of surveys (some qualitative, some quantitative), but he mentioned something I hadn’t ever thought about.

“For ordinal data, you always use the median average - for example, if you’ve asked ‘How satisfied are you with this feature?’ and given them the option of 1 through 5, median is the way to go!” (probably paraphrased)

Now I had never thought about this before - let’s do an example..

How satisfied are you with feature X of our product?

  1. Very dissatisfied
  2. Dissatisfied
  3. No opinion
  4. Satisfied
  5. Very satisfied

obviously, in this case, if the mean average gives 3.5, you’re going to have a hard time reporting “we’re somewhere in between [No opinion] and [Satisfied]”. So I suggested you could just translate the mean average into a percentage (in this case 70% satisfaction).. I understand why it’s not an optimal solution, but if you’ve set you’re outer options properly (the extreme case would be something like “I could not possibly be less satisfied” and “I could no possibly be more satisfied”) I’d argue it could be translated into percentage. I mean, you’re probably surveying to learn how you’re product could get better and whether you’re moving in the right direction. I’d also argue that your goal will always be to achieve 100% customer satisfaction - so now you know what you’re aiming at, and you’ve got a current point on your graph.. All you have to do now is make regular surveys, to tell if “feature X” is closing in on perfection..

“But why not just use median? Why be a bitch about it?”, you might ask.. Well, I’m not real keen on the whole obfuscating outliers deal.. If you have five respondents answering “1, 1, 5, 5, 5”, the median will give you 5, whereas the the mean average is 3 point something.. Now “5. Very satisfied” is very easy to dwell on, and might make look at improving less crucial features of your product.. But you’ve still got 20% of your client base, who are “Very dissatisfied” with the feature!

My conclusion is there are pros and cons in both cases, but unless you give me something more to take into account, I’ll take “hard to translate” over “forget about those guys” any day..!