Negative visitors
Seth Godin is a brainstorm in a teakettle, a one-man tornado of ideas and insight which I have a feeling would pick me up and fling me to Singapore if I got within three meters. That said, I’d like to know what site he’s referring to whose pages-per-visitor distribution has a mean of 2.1 and a median of 9. Unless it has a hell of a lot visitors viewing negative pages, which sounds kinda scary and more than a little sinister. Perhaps he meant mode rather than median? Or maybe he was exaggerating (to a mathematical impossibility) to make a point? Either way, it’s a little disturbing because his entire point is that people fail to understand what these measures indicate.
(Or am I completely deluded and it’s possible to have a mean which is less than half the median when one has a distribution composed entirely of positive numbers?)
September 18th, 2007 at 4:19 pm
You make an interesting point regarding the value of precise terminology, yet strangely, I did not have any difficulty understanding what Seth was talking about. Perhaps it is because I have seen that same pattern he was referring to in web site statistics, where you have a lot of brief visitors and a lot of extensive visitors to a website, but no middle ground. Nevertheless, I think you are technically correct.
It’s a lot like talking about the weather this week where I live. The high temperatures have been in the 90’s (F) and the lows have been in the 50’s.
Saying that the average temperature has been in the 70’s doesn’t quite capture the reality of the actual experience.
What words would you use to express this idea briefly?
September 18th, 2007 at 4:29 pm
Oh, I think his point was right and he explained it well — but by exaggerating the example to the point that it was actually impossible, I think the post might not only confuse people trying to understand the trend (e.g. — try to visualize the visitor graph that would cause that 2.1 vs. 9 case; you can’t), but also fail to drive home the real meaning of those terms. Understanding a particular trend is one thing, but understanding the concepts used to identify and describe it is even more important.
What’s really meaningful here is modes — one could describe these cases as multimodal, and communicate the trend in a word. Unfortunately modes are more difficult to collect and express concisely, at least compared to means and medians which can be distilled to a single number.
My point is just that when one’s talking about something as inherently subtle as statistics, which are notoriously confusing but incredibly powerful, one must take care not to abuse the terminology.
Here a picture is worth a thousand words to non-mathematicians. Unfortunately I’m too lazy^H^H^H^Hbusy to put together a good graphic at the moment.
September 18th, 2007 at 4:41 pm
So, guys, thanks for reading.
I actually made up the median in this example. you’re right it should be a lot lower in order to be possible, but the point is correct.
sorry.