How not to draw a graph

The Daily Mail had an article earlier this year reporting some research which stated that people are happy at the age of 15, gradually drop off in satisfaction until the age of 45, then get happier again until a peak at 74. There are a few potential problems I can see with the research (asking people to self-report on their happiness has always seemed pretty dodgy, and have they properly controlled for some years just being less happy than others?) But that's not the issue here. The issue is the "graph" they used to illustrate the research.

Let's have a look at it:

Yes, really. That is a genuine graph directly from the website (in fact, that picture is being hosted on their website, I couldn't be bothered to download it). Look at the scale... The horizontal axis doesn't have one! The distance from 15-40 is the same as the distance from 40-50! Why would anyone make the graph look like that? Would they really be unable to make the same point using a graph with sensible axes?

Let's have a look:

That doesn't really look any less impressive (apart from the fact that I drew it in about 10 minutes in GIMP, and the Daily Mail hires qualified graphics people), and the patterns are still pretty clear. The slight upward trend in the 40's starts before 46 (but that's also true on the Mail's original) and the *massive* peak at 74 does start to look a bit suspicious... could it be a small-numbers effect?

Why did the Mail choose to go with the inumerate version? Apart from the obvious, I genuinely can't see how theirs is better than mine on any dimension, and it's pretty obvious in which ways it's worse.

HT to Dave in the comments at BishopBlog