During a quarterly operations review, a logistics company evaluated 20

Question

During a quarterly operations review, a logistics company evaluated 20 distribution centers. Each center used either automated sorting or manual sorting, but not both, and was assigned to one of four size categories, with category 1 representing the smallest centers and category 4 the largest. For each center, the table shows whether automated sorting was used, the center's size category, and its scores for order accuracy, processing speed, and workplace safety. The overall performance score was calculated as a weighted mean of these three scores, using the same weights for every center.

Distribution center  
  Automated
sorting?
(Y/N)  
  Size
category  
  Accuracy
score  
  Speed
score  
  Safety
score  
  Overall
score  
 
  Alder 
 Y 
 2 
 88 
 84 
 90 
 87.8 
 
  Beacon 
 N 
 1 
 74 
 81 
 79 
 78.6 
 
  Cedar 
 Y 
 3 
 92 
 89 
 94 
 92.1 
 
  Delta 
 N 
 2 
 83 
 86 
 80 
 82.4 
 
  Elm 
 Y 
 1 
 69 
 75 
 82 
 77.3 
 
  Fulton 
 N 
 4 
 95 
 91 
 88 
 90.3 
 
  Grove 
 N 
 2 
 78 
 74 
 76 
 75.8 
 
  Harbor 
 Y 
 2 
 85 
 92 
 87 
 88.1 
 
  Iris 
 N 
 3 
 71 
 77 
 73 
 73.8 
 
  Juniper 
 Y 
 4 
 96 
 94 
 98 
 96.4 
 
  Keystone 
 N 
 1 
 82 
 68 
 72 
 72.8 
 
  Lakeview 
 Y 
 2 
 79 
 83 
 85 
 83.2 
 
  Mesa 
 N 
 3 
 88 
 85 
 90 
 88.1 
 
  Northgate 
 N 
 2 
 66 
 73 
 70 
 70.1 
 
  Orchard 
 Y 
 3 
 91 
 86 
 89 
 88.5 
 
  Pine 
 N 
 1 
 77 
 88 
 84 
 83.8 
 
  Quarry 
 N 
 4 
 84 
 79 
 81 
 81.0 
 
  Ridge 
 Y 
 1 
 73 
 80 
 76 
 76.6 
 
  Summit 
 N 
 2 
 90 
 93 
 91 
 91.4 
 
  Valley 
 N 
 3 
 81 
 76 
 78 
 78.0

For each of the following statements, select  Yes  if the statement is true based on the information provided; otherwise, select  No .

Bunuel · Accepted Answer

Official Solution:  
 
Statement 1: No

If the accuracy, speed, and safety scores were weighted equally, the overall score would simply be their arithmetic mean.

For example, for Alder:

(88 + 84 + 90)/3 ≈ 87.3

However, Alder's overall score is 87.8. Therefore, the three scores were not weighted equally, so the statement is  No .
 
Statement 2: Yes

A positive correlation means that as one variable increases, the other  generally tends to  increase as well, and as one decreases, the other  generally tends to  decrease.

Sort the table by accuracy score from lowest to highest and consider only the distribution centers marked “Y” for automated sorting. We can see that as the accuracy score increases from 69 to 96, the speed score generally tends to increase from 75 to 94.

Therefore, accuracy score and speed score are  positively correlated  among distribution centers using automated sorting, so the statement is  Yes .
 
Statement 3: Yes

For size-category 3 distribution centers, the overall scores from lowest to highest are:

73.8, 78.0, 88.1, 88.5, 92.1

The median is the middle value,  88.1 .

For size-category 2 distribution centers, the overall scores from lowest to highest are:

70.1, 75.8, 82.4, 83.2, 87.8, 88.1, 91.4

The median is the middle value,  83.2 .

Since 88.1 > 83.2, the median overall score for size-category 3 distribution centers is greater than that for size-category 2 distribution centers. Therefore, the statement is  Yes .
 
Correct answer: 
Statement 1: No
Statement 2: Yes
Statement 3: Yes

dhart · Answer

I think the answra look like 
1. Yes
2.No
3. Yes
f

officiisnobis · Answer

1 - If we do average of Northgate we get 67. something which is not equal to the overall score. So, NO
2 - YES
3 - size-category 3 distribution centers - 88
size-category 2 distribution centers - 83
YES

dhart · Answer

For 2. for Lakeview , Harobor and Adler the corelation takes a complete u - turn, so i think the answer should be No

Jyoti3380 · Answer

Yes, for Q2- had the sample was tiny...then maybe we could do YES however numbers are sort of equally distributed as in half of them are + correlated and others aren't.

Pls clarify.....if otherwise.

Yes	No
		For every distribution center, the overall performance score could have been obtained by taking the arithmetic mean of the accuracy, speed, and safety scores.
		Among distribution centers using automated sorting, accuracy scores and speed scores were positively correlated.
		The median overall score for size-category 3 distribution centers was greater than the median overall score for size-category 2 distribution centers.

During a quarterly operations review, a logistics company evaluated 20

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Distribution center	Automated sorting? (Y/N)	Size category	Accuracy score	Speed score	Safety score	Overall score
Alder	Y	2	88	84	90	87.8
Beacon	N	1	74	81	79	78.6
Cedar	Y	3	92	89	94	92.1
Delta	N	2	83	86	80	82.4
Elm	Y	1	69	75	82	77.3
Fulton	N	4	95	91	88	90.3
Grove	N	2	78	74	76	75.8
Harbor	Y	2	85	92	87	88.1
Iris	N	3	71	77	73	73.8
Juniper	Y	4	96	94	98	96.4
Keystone	N	1	82	68	72	72.8
Lakeview	Y	2	79	83	85	83.2
Mesa	N	3	88	85	90	88.1
Northgate	N	2	66	73	70	70.1
Orchard	Y	3	91	86	89	88.5
Pine	N	1	77	88	84	83.8
Quarry	N	4	84	79	81	81.0
Ridge	Y	1	73	80	76	76.6
Summit	N	2	90	93	91	91.4
Valley	N	3	81	76	78	78.0

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