This problem does not require the use of data mining software and focuses on knowledge of concepts and basic calculations. The Boleyn sisters, a pair of entrepreneurs who recently sold their start-up for a multi-million-dollar sum, are looking for alternate investments for their newfound fortune. They are considering an investment in wine, similar to how some people invest in rare coins and fine art. To learn more about the properties of fine wine, they have collected data on 13 different characteristics of 178 wines. They have applied k-means clustering to these data for a range of k values and generated the following table of average silhouette values and elbow chart. k Average Silhouette Value 2 0.259 3 0.285 4 0.260 5 0.231 6 0.194 7 0.206 8 0.197 9 0.156 10 0.202 An elbow chart has a horizontal axis labeled "Number of Clusters" with values from 0 to 11 and a vertical axis labeled "Total Within-Cluster Sum of Squares" with values from 0 to 2,600. The elbow chart has 10 points connected by line segments. A pattern goes down and right becoming less steep from (1, 2,500) to (10, 880). The points are as follows. (1, 2,500) (2, 1,730) (3, 1,390) (4, 1,250) (5, 1,190) (6, 1,120) (7, 1,050) (8, 1,000) (9, 950) (10, 880) (a) Which value of k appears to be the most appropriate to categorize these wines? k = (b) Because the average silhouette values are low for all values of k, the Boleyn sisters are concerned about the quality of their clustering results. What experiments could they conduct to potentially improve the clusters?

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter2: Working With Real Numbers

Section2.3: Rules For Addition

Problem 8P

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This problem does not require the use of data mining software and focuses on knowledge of concepts and basic calculations.

The Boleyn sisters, a pair of entrepreneurs who recently sold their start-up for a multi-million-dollar sum, are looking for alternate investments for their newfound fortune. They are considering an investment in wine, similar to how some people invest in rare coins and fine art. To learn more about the properties of fine wine, they have collected data on 13 different characteristics of 178 wines. They have applied k-means clustering to these data for a range of k values and generated the following table of average silhouette values and elbow chart.

k	Average Silhouette Value
2	0.259
3	0.285
4	0.260
5	0.231
6	0.194
7	0.206
8	0.197
9	0.156
10	0.202

An elbow chart has a horizontal axis labeled "Number of Clusters" with values from 0 to 11 and a vertical axis labeled "Total Within-Cluster Sum of Squares" with values from 0 to 2,600. The elbow chart has 10 points connected by line segments. A pattern goes down and right becoming less steep from (1, 2,500) to (10, 880). The points are as follows.

(1, 2,500)
(2, 1,730)
(3, 1,390)
(4, 1,250)
(5, 1,190)
(6, 1,120)
(7, 1,050)
(8, 1,000)
(9, 950)
(10, 880)

(a)

Which value of k appears to be the most appropriate to categorize these wines?

k =

(b)

Because the average silhouette values are low for all values of k, the Boleyn sisters are concerned about the quality of their clustering results. What experiments could they conduct to potentially improve the clusters?

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