Archive for January, 2014

The Friendship paradox not explained by position of median

January 18, 2014

The fascinating story of the Friendship paradox, and two examples to show that knowing whether the median is higher or lower than the average, doesn’t help explain the paradox. Just a recap for myself. The median is the value of dividing the sample in half and looking at the highest value of the lowest set averaged with the lowest value of the highest set… or the middle one. The mode is the most recurring value in the sample.

The way to read

A:BX

means that A is friends with B and X

First example – median higher than average

A:BX 3,5=4 <---------list of each friend's count, then average friend count after =
B:ACX 2,3,5=10/3
C:BDX 3,3,5 = 11/3
D:CEX 3,2,5=10/3
E:DX 3,5=4
F:G 1
G:F 1
X:ABCDE 2,3,3,3,2=13/5
Median = 3 friends
Mode = 3 friends
Average friends. = 2.5
Friend's average = 2.866

2nd example – median lower than average

A:BX 3,4 = 7/2
B:ACX 2,3,4=3
C:BDX 3,2,4=3
D:CX 3,4=7/2
E:FG 2,2=2
F:EG 2,2=2
G:EF 2,2=2
H:IK 2,2=2
I:HK 2,2=2
K:HI 2,2=2
X:ABCD 2,3,3,2=10/4

median = 2
mode = 2 
average friends = 2.363636
Friend's average = 27.5/11= 2.5
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