As part of the quarterly reviews, the manager of a retail store analyzes the quality of customer service based on the periodic customer satisfaction ratings (on a scale of 1 to 10 with 1 = Poor and 10 = Excellent). To understand the level of service quality, which includes the waiting times of the customers in the checkout section, he collected the data shown below on 100 customers who visited the store.
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Customer Number
Wait Time (min)
Purchase Amount ($)
Customer Age
Customer Satisfaction Rating
1
2.3
436
42
7
2
2.8
408
33
6
3
3.2
432
38
5
4
3.4
431
40
5
5
3.4
456
29
6
6
4.2
537
46
4
7
3.2
456
42
5
8
1.4
430
40
8
9
6.4
663
24
3
10
7.8
839
37
4
11
6.5
659
52
5
12
9.8
836
43
2
13
5
543
56
4
14
1.8
419
35
8
15
6.1
700
39
6
16
3.4
432
44
7
17
7.8
845
33
5
18
2.8
467
42
6
19
1.2
425
46
8
20
9.5
848
50
4
21
8.2
808
55
3
22
7.6
674
35
3
23
5.4
547
52
4
24
6.7
691
38
5
25
9.6
847
53
4
26
11.4
826
48
2
27
2.1
426
52
7
28
5.6
535
32
7
29
3.7
521
43
8
30
4.9
513
44
6
31
6.4
645
53
5
32
9.3
846
52
4
33
10.6
730
51
3
34
6.5
786
53
3
35
5.4
523
46
5
36
7.6
654
36
6
37
3.2
443
48
7
38
2.4
409
54
8
39
1
400
39
6
40
0.2
418
51
7
41
2.4
498
30
6
42
5.7
532
32
5
43
6.4
663
44
7
44
6
681
39
8
45
3.7
543
54
5
46
8.7
800
51
5
47
6.9
673
45
5
48
9.8
856
43
4
49
10
756
44
4
50
9.5
854
43
6
51
6.3
672
50
6
52
7.4
698
47
7
53
2.3
434
43
7
54
4.6
544
40
4
55
4.9
523
53
6
56
5.7
546
55
6
57
7.4
676
42
8
58
6.8
662
36
6
59
9.6
1000
40
5
60
6.4
678
46
5
61
7.2
655
32
4
62
5.6
535
36
5
63
9.7
833
35
3
64
2.3
498
30
7
65
4.3
508
41
6
66
5.7
542
49
6
67
2.4
435
39
8
68
6.7
665
41
5
69
2.4
387
54
9
70
9.8
845
34
7
71
4.5
532
40
6
72
6.7
687
30
5
73
7.2
643
33
4
74
3.5
424
49
7
75
8.9
836
47
5
76
9.7
876
31
4
77
3.5
456
47
7
78
4.7
523
49
6
79
8.5
818
35
5
80
9.7
845
54
4
81
2.7
401
55
7
82
5.7
554
43
6
83
7.6
648
51
7
84
4.4
540
31
6
85
7.8
839
45
5
86
9.4
845
48
4
87
4.9
534
36
5
88
7.1
693
44
4
89
5.4
512
39
3
90
6.7
665
49
5
91
8.6
825
36
5
92
4.5
548
30
7
93
6.1
704
31
5
94
5.3
509
31
6
95
6.7
672
35
5
96
8.1
824
36
4
97
6.3
632
30
4
98
7.4
689
35
2
99
8.8
839
50
4
100
9.6
847
35
2
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Using the data given, apply hierarchical clustering with five clusters using Wait Time (min), Purchase Amount ($),
Customer Age, and Customer Satisfaction Rating as variables. Be sure to Normalize input data in Step 2 of the
XLMiner Hierarchical Clustering procedure. Use Ward's method as the clustering method.
a. Use a PivotTable on the data in the HC_Clusters1 worksheet to compute the cluster centers for the five clusters
in the hierarchical clustering.
b. Identify the cluster with the largest average waiting time. Using all the variables, how would you characterize
this cluster?
c. Identify the smallest cluster.
d. By examining the dendrogram on the HC_Dendrogram worksheet (as well as the sequence of clustering stages
in HC_Output1), what number of clusters seems to be the most natural fit based on the distance?
What will be an ideal response?
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b. Cluster 5 has the largest average waiting time (approx. 9.35 min).
This cluster is a collection of 11 customers characterized by the largest average purchase
amount of about $823, the oldest average customer age, and the lowest average customer
satisfaction rating 3.36.
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c. We see that the size of the clusters does not vary much. However, Cluster 5 is the smallest
cluster with a collection of 11 customers.
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d. From the below figure, four clusters appear to be a natural fit for this data. When there are
more than four clusters, mergers result in a small marginal increase in distance, but when there
are less than four clusters, mergers lead to a large marginal increase in distance.
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