A couple of minutes later another graph appeared. It was roughly similar but roughly in the roughest sense of the word. If that second graph was a bottle, it was a bottle of stout, a small squat one at that.
The two graphs represented two different human realities in Ireland. They were part of a presentation by the Central Statistics Office on its analysis of demographic trends from the 2006 Census.
Both of these graphs reflected life expectancy. The first graph depicted the 'settled' population. It showed - unsurprisingly - that people are living longer, hence the elegant long neck.
The second graph was truly shocking. It reflected the same set of statistics as they related to travellers. The proportion of travellers under the age of 20 is enormous but the fall-off after that is shocking, truly shocking. The percentage of travellers who can hope to live behind the ages of 60 is tiny, beyond 70 infinitesimally small, and beyond 80, almost non-existent. Thus, the small squat stout bottle.
The grim and obvious truth is that there's a section of Irish society who, on average, can expect to live up to two decades less than their settled counterparts. That's more than shocking. It's a scandal.
Now, in fairness, the CSO statisticians entered a couple of caveats. The questions relating to travellers in the latest census were new ones that gave rise to variances and certain unreliabilities of comparison. For example, the birth rates, says the CSO, suggests that the actual population of travellers is perhaps a couple of thousand higher than the actual figures. The corollary is that the lower life expectancy figures may also be slightly skewed.
But only slightly. When you see these graphs - the elegant long-necked bottle and the fat squat stout bottle - the only word that can form on your lips is scandal.
This week, the junior minister with responsibility for equality Frank Fahey announced the identity of those who would be on the National Traveller Monitoring and Advisory Committee.
This is not to beat Fahey who has proven to be more pro-active than most other ministers in this regard (with the exception of Chris Flood). But if you look at the ancient beginnings of this committee and its eventual destination way off in the future, it tells a tale of the inertia and inaction that characterises non-priority stuff for government.
Bear with me for a couple of seconds because while the following prose mightn't whizz off the page, it is important. Way back in 1995 - that's 12 years ago - a task force on the travelling community reported its findings. A committee called the traveller monitoring committee was set up to monitor implementation of its recommendations and ten years later produced its second and final progress report.
So what was produced in that decade between 1995 and 2005? What great benefit was derived by society and by its travelling community? This is the equality department's own language describing the situation as it was in 2005: "There was a general view that it needed to be revitalised and made into a more dynamic and forward looking national forum."
In other words, not much happened that made a difference to the lot and lives and status of travellers. And so now we have a new initiative. And it's worthy. And it's headed up by a well-respected former civil servant, Kevin Bonnar. And part of its mandate will be to oversee strategies that increase the participation of travellers in wider society, including finding employment opportunities.
But then, it's part of the Towards 2016 partnership agreement. And when I see the date 2016, I automatically think of long-fingering and another report being produced that year telling us all that we haven't done enough and saying we should all do more to improve the lot of travellers.
Examiner columnist and Barnardos chief executive Fergus Finlay put it well this week, when talking about another group on the margins of priorities, children.
"I've been involved in writing political manifestos before and I know that at the last minute someone says, 'We need to throw something in there about children'. So it ends up on page 40 of the manifesto."
Because the grim reality is that tangible and real improvements for marginalised people in Irish society can only happen if there is real political will. And for travellers, for those with mental illness, for families who have children with autism, or intellectual or other disabilities, or for the poor and dispossessed, children and adults, there is no real political will.
Political parties pay a lot of lip service to it. But they know that people are more likely to vote with their pockets rather than their conscience.
This is my column from today's Irish Examiner