Revision as of 22:12, 26 May 2023 by Admin (Created page with "'''Key: C''' The means for cluster 1 are (1 + 0 + 6)/3 = 2.3333 for X<sub>1</sub> and (3 + 4 + 2)/3 = 3 for X<sub>2</sub> and the variation is (1 − 2.3333)<sup>2</sup> +...")
Exercise
ABy Admin
May 26'23
Answer
Key: C
The means for cluster 1 are (1 + 0 + 6)/3 = 2.3333 for X1 and (3 + 4 + 2)/3 = 3 for X2 and the variation is
(1 − 2.3333)2 + (3 − 3)2 + (0 − 2.3333)2 + (4 − 3)2 + (6 − 2.3333)2 + (2 − 3)2 = 22.6667.
The means for cluster 2 are (5 + 1)/2 = 3 for X1 and (2 + 6)/2 = 4 for X2 and the variation is
(5 − 3)2 + (2 − 4)2 + (1 − 3)2 + (6 − 4)2 = 16.
The total within-cluster variation is (per equation (10.12) in the first edition of ISLR)
2(22.6667 + 16) = 77.33.
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.