
Raw results are available here
No surprise, the high water mark was April 2015 general conference just before Packer, Perry, and Scott joined the choir eternal. The average age in April 2015 was 79.5 years old. The lowest average age of all apostles was 28.8 years old in 1835 when the apostles were first called starting with the much maligned Thomas Marsh.
I think it would be a bit overstepping bounds to draw too many conclusions. But modern medicine in the 20th century helped the age along coinciding with some of the more dramatic exits from the quorum due to the end of polygamy. Also noticeable is the unbroken line from April 1995 (Henry Eyring joins Q15) through October 2004 (Dieter Uchtodorf joins Q15). This is the longest period of no changes to the quorum throughout almost two centuries.
Demographic attitudes based on age are perhaps another interesting, but less precise topic. The average age of high school graduation of current apostles is class of '59 (2016 - 75 = 1941. 18 years past 1941). So the bulk of the quorum came of age in the 1960s and were very likely ensconced in the BYU counter counter culture established by Ernie Wilkinson's additions to the BYU Honor Code.
I used Python 3.4 to write this script. The full source and data is available and I will gladly rebuild the results if anyone detects an error in my coding. If you come up with some additionally intriguing questions based on publicly published data I could easily be persuaded to produce more graphs.