First off, I used the Julian calendar because it makes this sort of study easier. The Julian calendar assigns consecutive dates for each day starting with day 1 (January 1st) and ending with day 365 (December 31st most years). So, in analyzing a series of numbers like ice-out dates, there are three characteristics engineering types look for:

Mode: the most common number in the list, in this case the date on which ice-out has occurred most often. For Rangeley we, have a tie between May 4th and May 11th

Mean: also known as the average. May 7th it is!

Median: arranging the list in rank order (for ice out earliest to latest), the number/date in the middle of the list is the median. This characteristic is not particularly informative for ice out data and it pretty much matches the average.

Attached is my study, the utility of which is constrained by several factors:
Input error by me (garbage in = garbage out!)
The arbitrary and capricious nature of the official ice-out declaration. It is not only subjective, it is hard to observe the condition of the ice during the hours between sunset and sunrise!
This is a pathetically poor sample both in size and data distribution (we only have the last 140 consecutive years). Rangeley Lake has existed, more or less in its current state, for well over 12,000 years. We have no data for years 1 thru 11,860!! Imagine you watched only the last play of the last 140 football games. What would that tell you? The answer is: Nothing
For the purpose of ice-out, our calendar has a huge error built in: It takes the Earth 365 days plus 6 hours to orbit the Sun. So unless you record the time of ice-out and then add the requisite correction factor, (which, in 25% of the years, is 18 hours!) what you have is a date plus or minus one day.
But if your objective  is to win the Highlander ice-out contest, this data is gold. Please remember me when you win.

Caution: Connecting the ice-out date with ambient temperature conditions ignores many other factors that influence ice-out. Wind and late season snow events being two of the biggies. I think it was last year that ice-out was unexpected early (May 11) and was caused by a big wind. The moving, unmelted, ice sheet did a lot of damage to shorelines and docks.

Rangeley Ice Out Dates
						Earliest to Latest
1880		134				104	April 14th or was it really April 15th?
		136				104
		144				106
		136				106
		134				109
		136				111
		124				112
		137				113
		142				113
		120				114
		129				114
		134				115
		130				115
		137				116
		122				116
		127				116
		131				117
		133				117
		125				118
		128	ave	132	May 12th	119
						119
1900		136				119
		124				119
		118				119
		117				120
		135				120
		125				120
		133				120
		139				121
		131				121
		132				121
		109				121
		131				122
		130				122
		124				122
		141				122
		119				122
		129				122
		137				123
		123				123
		123				123
			ave	128	May 8th	123
1920		140				124
		104				124
		124				124
		129				124
		131				124
		119				124
		138				124
		119				125	Mode 1 May 5th 10 times
		134				125
		130				125
		126				125
		116				125
		127				125
		127				125
		125				125
		131				125
		125				125	Mode 1
		131				126
		119				126
		134				126
			ave	126	May 6th	126
1940		140				126
		116				126
		125				126	Median	6-May
		140				127	Median	7-May
		132				127
14-Apr		104				127
		122				127
		133				127
		122				127
		114				127
		128				127
		122				128
		123				128
		114				128
		126				128
		120				128
		136				129
		121				129
		127				129
		128				129
			ave	125	May 5th	129
1960		125				130
		135				130
		137				130
		127				130
		127				130
		129				130
		137				131	Mode 2 May 11th 10 times
		130				131
		116				131
		132				131
		135				131
		135				131
1972		144				131
		124				131
		135				131
		132				131	Mode 2
		119				132
		127				132
		137				132
		121	ave	130	May 10th	132
						133
1980		126				133
		120				133
		133				133
		126				133
		125				133
		130				134
		117				134
		111				134
		126				134
		131				134
		125				135
		121				135
		133				135
		122				135
		128				135
		125				136
		130				136
		133				136
		113				136
		123				136
			ave	125		137
2000		121				137
		126				137
		115				137
		126				137
		124				137
		127				138
		113				139
		131				140
		125				140
		115				140
		106				141
		124				142
		106				144
		122				144	May 24th	or was it really May 23rd?
		131
		128
		112
		120
		129
		131
			ave	122
			140 yr ave	127	May 7th

Contribution by Bill Pierce is the following graph:

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