The distribution of online data usage

AT&T has recently announced it will no longer offer unlimited data plans for new iPhone users in the US, and now some carriers in the UK have followed suit. In each case, the providers claim that only a very small number of users actually use enough data to warrant an unlimited plan, and most users use relatively little and will benefit from the cheaper, capped plans. But what does "most users" mean? Journalist Charles Arthur of the Guardian, in an article about the impact of the data caps, illustrated the distribution of data usage amongst mobile users with this chart, created in R:

Reader Barry Rowlingson thought this chart looked odd (is that really a 97% percentile?), but given that the chart lacks axis labels, it’s hard to make sense of anyway. So he set to recreate the chart: given the mean (200Mb) and one quantile (the 97% quantile is 500Mb), he figured out the unstated standard deviation of the Normal distribution (159Mb) and recreated the graph with axis labels:

ss=seq(0,700,len=100)
plot(ss,dnorm(ss,mean=200,sd=159),col="red",type="l")
abline(v=500,col="black")

 
I added the black vertical line to indicate the 97% percentile at 500Mb. Anyway, it’s nice that R is being used to illustrate statistical concepts like this, just a shame that the chart wasn’t quite right. Thanks to Barry for providing this alternative.

The Guardian: Why file-sharing has killed ‘unlimited’ mobile data contracts