After General Conference was over my mother (who was visiting to help out with our new baby) remarked about how most of the Apostles had only a few kids. Being a scientist and a bit compulsive about my statistics I put together a little spreadsheet with the number of children each apostle has from which I calculated the mean, median, and mode number of children. My mother was correct in that more apostles have 3 children than any other number; however, the mean (4.93) and median (4.0) are higher.
Here are the numbers (Apostles are sorted according to seniority):

Anyone surprised by the numbers? I was that the mode was 3 but my guess of the average was 5, which is what the mean turned out to be. We cannot really throw out Elders Packer and Nelson as outliers because the sample size is small, plus it would defeat the purpose of the analysis to remove them from the analysis just because they create a slight positive skew to the data (skewness = 0.85, kurtosis = 0.30). In any case, I think it is interesting that 9 of the 15 apostles have 5 or fewer children (most of those 9 have 2 or 3 children). The rest have 6, 7, or 10. There is a moderate correlation between number of children and age (r=0.49, p=0.06; should you feel a nonparametric correlation is more appropriate, Spearman’s rho = 0.40, p = 0.14).
When I looked at the above chart, it looked like there were two clusters of apostlesXchildren based on seniority. I thus created two groups within the Apostles based on seniority; the 7 most senior (through Elder Scott) were one group and the 8 left were the other group (beginning with Elder Hales). This group split was as close to a median split as possible. A ttest revealed that there was a significant difference in the number of children between groups (mean for group 1 = 6.57, mean for group 2 = 3.5, t = 2.68, p = 0.02, Cohen’s d = 1.35 – a large effect). There also is a significant difference in age between the two groups (which is not surprising; group 1 mean = 83.57, group 2 mean = 68.38, t = 4.99, p = 0.001).
Should my split of the groups be criticized based on the fact that Elder Hales only has 2 children and so placing him in group 2 might be undue manipulation of the data, here are the values with him in group 1 (group 1 mean number of children = 6.00, group 2 = 3.71, t = 1.79, p = 0.097; this is no longer significant but the sample size is also small {although, it could be viewed as large because the entire population of living apostles is 15 and I ‘sampled’ the entire population}. In any case, the effect size of this difference is still large – Cohen’s d = 0.95). I think the split should be between Elder Scott and Elder Hales because Elder Hales is the first of the apostles called while Pres. Hinckley was the prophet (technically, Elder Hales was called to fill the vacancy in the Twelve when Pres. Hunter died; Pres. Hinckley was called to replace Pres. Hunter); in other words, Elder Scott was the last of the apostles called in the 1980s and Elder Hales was the first called in the 1990s (there was about a 6 year gap in between when they were called). Either way I split the groups, the difference in number of children is large between the more senior Apostles and the newer Apostles. There are the outliers in the groups (Pres. Monson and Elder Perry for group 1 and Elder Eyring for group 2) but overall, the groups cluster together well (see the “Within Cluster Variation” chart).
If seniority roughly equals age (remember the significant difference between the ages of the two groups), does age explain the difference in number of children? In part it does. Age explains 24% of the variance in number of children (R = 0.49, F = 4.166, p = 0.06), which is a moderate amount but it is obvious that age alone cannot account for the difference in number of children. There are other testable (e.g., number of children in their nuclear family, age at marriage, income, etc.) and untestable (e.g., personal choice and how many children the Lord let them know they could or should have) factors that might explain the difference. Frankly, it does not matter in the end. Can we really explain why people have the number of children that they have? Sometimes we can if there are fertility issues but the number of children a couple has boils down largely to personal choice. That is why I am not going to try to explain why we see these differences in the number of children between the more senior Apostles and the newer Apostles.
I hope you found this an interesting analysis – I certainly did! I think it would be interesting to expand it to include the 1st and maybe 2nd quorums of the Seventy as well but that is an analysis for a later time.