Earlier quoted context omitted.
I did a search for the number 14 and 16 without seeing anything that matched the claim. The closest I saw was "These men averaged thirty-six years of age (range: 24-60) and had been married an average of ten years (1-32 years) before marrying a second wife of a mean twenty-five years of age (14-39 years). At that time, their legal wives averaged thirty-two years of age (22-56)."
I don't think that claim is about Joseph Smith and marriages while he was alive, because polygamy wasn't official church doctrine then. I haven't found a good dataset, but this book has this comment: "Latter-day Saints were surprisingly obedient to the counsel to marry, and in 1860 Manti, only 1.6 percent of women over the age of 16 had never been to the altar." I believe 14 was the minimum legal age of marriage for…
I've always wondered at the historical accuracy of "A Study In Scarlet", but its depiction of the social climate regarding marriage among the LDS would appear to be spot-on...