I might have a thing here.
In the second row there are the following Flags with the dates of foundation / independency
UN: 1945 (Foundation)
Germany: 1949 (Federal Republic)
Austria: 1945 (Second Republic)
Slovenia: 1991 (Independence)
The arithmetic mean of those four dates is $$(1945 + 1949 + 1945 + 1991) / 4 = 1957.5$$. In the year 1975 the Saarland got re-connected with Germany
So here are the data for the whole bunch of Flags
Note: I used a standardized search on Google which gave me some different numbers
Row 1
Chile: September 18, 1810
Bolivia: August 6, 1825
Netherlands Antilles: 1954
US Virgin Islands: March 31, 1917
Row 2
United Nations: October 24, 1945
Germany: October 3, 1990
Austria: July 27, 1955
Slovenia: October 29, 1918
Row 3
Bosnia Herzegovina: March 1, 1992
Eritrea: April 27, 1993
Ethiopia: August 21, 1995
Armenia: September 21, 1991
Row 4
Armenia: September 21, 1991
Somalia: 2500 BC
Yemen: October 30, 1918
British Indian Ocean Territory: 1965
Nepal: September 25, 1768
Here's the number crunching part
Row 1
$1810 + 1825 + 1954 + 1917 = 7506$
$7506 / 4 = 1876,5$
Row 2
$1945 + 1990 + 1955 + 1918 = 7808$
$7808 / 4 = 1952$
Row 3
$1992 + 1993 + 1995 + 1991 = 7971$
$7971 / 4 = 1992,75$
Row 4
$1991 - 2500 + 1918 + 1965 + 1768 = 5142$
$5142 / 5 = 1028,4$
I don't know. if this is pointing in the right direction
Maybe it could be related to the UN itself, but the US Virgin Islands and the British Indian Ocean Territory and the Netherlands Antilles are not members of th UN