But instead of simply bemoaning the lack of statistical information, lets take a step in a more positive direction. Name a statistical measure of anything related to the LDS Church that would tell you something that you thought would shed light on the current health and progress of the Church, or would simply scratch some nagging itch in your own mind.
There are only two rules:
1. You do not have to pick a statistic that you know is actually collected in real life (either by the Church or by some other party); however, pick a measure that could conceivably be collected and reported in some kind of comprehensive and accurate way. A bad example of this would be: "I want to know the number of sacrament cups used worldwide each week as a proxy for how many worthy members of the Church attend their Sabbath services." This statistic does not work because it is difficult to see a) how this statistic would be collected, and b) even if it could be, how accurately the statistic would reflect on the purpose of its collection. It would be inconceivable to put an observer in every meeting of the Church each week to see how many people are taking the sacrament. Someone might suggest using instead the number of sacrament cups ordered by each unit. However, I do not know whether all units in the Church worldwide order sacrament cups from the same distributor (probably the Church). Furthermore, even if good information on the orders was available, Church units certainly keep an unused inventory of the cups, so it would be hard to determine how many of them were actually used given that unused cups are probably thrown away each week after the sacrament.
2. Don't pick financial information. Its an arbitrary rule, but a sound one. Beyond the fact that I am not sure that financial or budgetary information qualifies as a statistic, this answer is just a cop-out. We're all curious. We would probably all want to know how much $ the Church has, or how much it spends on BYU, temples, etc. So try thinking a little harder about it.
Answering the question for myself, I would love to see the numbers on the net number of temple marriages contracted each year. To show what I mean by net, I mean only living members of the Church (no proxy sealings counted), and subtract out all divorces by Church members (both civil and temple but only count each divorce once) and any occurrence where a temple-married member has their name removed from the records of the Church. Exclude also any second temple marriages for persons over the age of 50. In my opinion, getting married in the temple is a good proxy for the general spiritual health of the Church membership, especially for the youth. No doubt an imperfect one, but likely the best that would be available. This information could easily be gathered from the Church's records department and would not likely include any investigation outside official Church records. As far as why I made the choices I did on delineating the metric, I think it ought to be clear why sealings for the dead are excluded. I want divorces subtracted because of course, if temple marriage signals the formation of a family (the fundamental unit of the Church...and of society, as Church leaders continuously remind us), then divorce signals the dissolution of that family. Because a dissolution of the sealing bond sometimes occurs some time after a civil divorce is finalized (except possibly in the case of major transgression), and in some circumstances that I am aware of, sealing bonds are not dissolved until the remarriage of one of the partners (usually the female), we need to account for civil divorces. I waffled on counting name removal the same as divorce. Technically speaking the sealing bond should be broken, but if a name is removed for excommunication pursuant to transgression, then it may still be that the family remains together, the transgressor is rebaptized and the sealing "reactivated." In that case, we count both the name removal and the re-sealing, and it comes out a wash. The reason why I exclude second marriages involving members over 50 is that usually these occur when one party to the original marriage dies, but after a great deal of the child rearing is complete. I do not think that it indicates how healthy the Church is spiritually or how well the youth are absorbing the lessons on the importance of temple marriage that an older widow or a widower finds another mate. Thus, a young adult who marries in the temple, but is later divorced from the first spouse or whose first spouses dies, and then remarries soon thereafter to another young adult, gets counted. This is a new family, and one that still reflects the purpose for which the statistic is collected. However, Elder Nelson's recent remarriage following the death of his wife, would not be counted.
So you have now read the above too-long justification for my own choice. Of course, there are literally dozens of statistics I would like to see other than the one described above. What would you choose and why?