Obscure statistics
Posted: 19:01 Sun 30 Sep 2007
Imagine a bulletin board with 4 members, whose number of posts are 1000, 1000, 1000 and 1. How many members does this bulletin board have? Well, really, in an activity-weighted sense, 3.
Mathematically the natural way to capture this is (∑)²/(∑²), that is, the square of the sum divided by the sum of the square: 1000+1000+1000+1 = 3001; 1000²+1000²+1000²+1² = 3000001; so (∑)²/(∑²) = 3001Ã 3001÷3000001 ≈ 3.002.
As of a few moments ago ThePortForum.com’s members had post counts of 1050, 812, 600, 550, 325, 303, 224, 223, 175, 71, 61, 55, 51, 48, 42, 39, 31, 23, 22, 20, 18, 17, 11, 7, 6, 6, 5, 4, 3, 2, 0, 0, 0. (∑)²/(∑²) = 4804Ã 4804÷2775568 ≈ 8.3148: so TPF has, activity-weighted, slightly more than eight members.
As another example, a different web BB that need not be named here, of more ancient provenance than this one and hence with a longer tail of members, a few moments ago had post counts of 3064, 2290, 1697, 1373, 991, 975, 622, 395, 392, 372, 366, 342, 331, 321, 305, 271, 221, 210, 162, 158, 145, 139, 138, 132, 126, 125, 121, 116, 114, 111, 110, 102, 101, 99, 94, 93, 90, 87, 85, 79Ã 2, 78Ã 2, 75, 72, 67, 64Ã 2, 63, 61, 59, 57, 56, 55Ã 3, 51, 49, 48Ã 2, 47, 46Ã 2, 45Ã 3, 44, 40, 39Ã 3, 38Ã 3, 37, 36, 35, 34, 33Ã 3, 32, 31Ã 2, 29, 28Ã 3, 26Ã 4, 25, 24Ã 4, 23Ã 3, 22Ã 4, 21Ã 8, 19, 18Ã 3, 17Ã 5, 16Ã 3, 15Ã 3, 14Ã 2, 13Ã 2, 12Ã 11, 11Ã 2, 10Ã 9, 9Ã 8, 8Ã 10, 7Ã 8, 6Ã 10, 5Ã 17, 4Ã 24, 3Ã 35, 2Ã 52, 1Ã 69, and a load of zeroes. So (∑)²/(∑²) = 21162Ã 21162÷23331130 ≈ 19.1945.
Mathematically the natural way to capture this is (∑)²/(∑²), that is, the square of the sum divided by the sum of the square: 1000+1000+1000+1 = 3001; 1000²+1000²+1000²+1² = 3000001; so (∑)²/(∑²) = 3001Ã 3001÷3000001 ≈ 3.002.
As of a few moments ago ThePortForum.com’s members had post counts of 1050, 812, 600, 550, 325, 303, 224, 223, 175, 71, 61, 55, 51, 48, 42, 39, 31, 23, 22, 20, 18, 17, 11, 7, 6, 6, 5, 4, 3, 2, 0, 0, 0. (∑)²/(∑²) = 4804Ã 4804÷2775568 ≈ 8.3148: so TPF has, activity-weighted, slightly more than eight members.
As another example, a different web BB that need not be named here, of more ancient provenance than this one and hence with a longer tail of members, a few moments ago had post counts of 3064, 2290, 1697, 1373, 991, 975, 622, 395, 392, 372, 366, 342, 331, 321, 305, 271, 221, 210, 162, 158, 145, 139, 138, 132, 126, 125, 121, 116, 114, 111, 110, 102, 101, 99, 94, 93, 90, 87, 85, 79Ã 2, 78Ã 2, 75, 72, 67, 64Ã 2, 63, 61, 59, 57, 56, 55Ã 3, 51, 49, 48Ã 2, 47, 46Ã 2, 45Ã 3, 44, 40, 39Ã 3, 38Ã 3, 37, 36, 35, 34, 33Ã 3, 32, 31Ã 2, 29, 28Ã 3, 26Ã 4, 25, 24Ã 4, 23Ã 3, 22Ã 4, 21Ã 8, 19, 18Ã 3, 17Ã 5, 16Ã 3, 15Ã 3, 14Ã 2, 13Ã 2, 12Ã 11, 11Ã 2, 10Ã 9, 9Ã 8, 8Ã 10, 7Ã 8, 6Ã 10, 5Ã 17, 4Ã 24, 3Ã 35, 2Ã 52, 1Ã 69, and a load of zeroes. So (∑)²/(∑²) = 21162Ã 21162÷23331130 ≈ 19.1945.