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GMAT695
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Joshidivya
Can someone please explain me the answer
Fairly simple question.

First sort the table each category wise in ascending order and then look at the 3rd and 4th value in the column for each category.

You need to check whether median will be changed if any additional values are added to the data set , if yes then you mark Yes, else No.

For eg. take case of flavor.

ProductFlavorAppearancePrice
B115
E214
F251
A435
C531
D554

current median is 3 (sum of 3rd and 4th value divided by 2). Now if you add the rating of seventh product as 2 then you median as 2 so median changed by adding the 7th value. So mark YES. Similarly repeat for all the products.
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GMAT695
For each of Six ready-to-eat food products, the table shows a particular product tester’s ratings—ranging from strongly negative (1) to strongly positive (5)—in each of three categories.

ProductFlavorAppearancePrice
A435
B115
C531
D554
E214
F251

Suppose that this product tester was to give ratings for a seventh ready-to-eat food product. For each of the following categories, select Yes if the addition of the ratings for the seventh product could change the median rating in that category. Otherwise, select No.

The question deals with concept of median, which depends on the number of elements in a set.

If there are even number of elements, median is the average of the middle two.
If there are odd number of elements, then median is the central value, which can be found by (n+1)/2, where n is the number of elements.

Here, we have six elements, so median is middle of 3 and 4 elements, and for median to remain unchanged by addition of new element, the 3 and 4 elements of the initial set should be equal. That is 3rd = 4th = (3rd+4th)/2
Reasoning is in the video below.

Answer No, Yes, Yes


Attachment:
GMAT-Club-Forum-ajr4nvmt.png
GMAT-Club-Forum-ajr4nvmt.png [ 205.31 KiB | Viewed 1611 times ]
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In an attempt to generalize this result, Let take two cases:
If the Data set looks like .....X,X..... ie middle most values are same.
(A) n is even..median is X..introducing any value larger,smaller or Equal to X will not change the mean.
(B) n is odd..median is X..Introducing ..its possible the value may or may not change even if the introduced value is more or less than X (depends where the two x were repeated).

Can anyone help me complete this hypothesis?
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Your answers seem to be the opposite. I was confused when I did the problem then I saw your answer choices. Just a heads-up.
chetan2u
GMAT695
For each of Six ready-to-eat food products, the table shows a particular product tester’s ratings—ranging from strongly negative (1) to strongly positive (5)—in each of three categories.

ProductFlavorAppearancePrice
A435
B115
C531
D554
E214
F251

Suppose that this product tester was to give ratings for a seventh ready-to-eat food product. For each of the following categories, select Yes if the addition of the ratings for the seventh product could change the median rating in that category. Otherwise, select No.

The question deals with concept of median, which depends on the number of elements in a set.

If there are even number of elements, median is the average of the middle two.
If there are odd number of elements, then median is the central value, which can be found by (n+1)/2, where n is the number of elements.

Here, we have six elements, so median is middle of 3 and 4 elements, and for median to remain unchanged by addition of new element, the 3 and 4 elements of the initial set should be equal. That is 3rd = 4th = (3rd+4th)/2
Reasoning is in the video below.

Answer No, Yes, Yes


Attachment:
GMAT-Club-Forum-ajr4nvmt.png
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in price- if the rating is 5 then the median would be 4+5/2=4.5, then why no?
Shafkat26
Flavor: 1,2,2,4,5,5. Median = (2+4)/2 = 3
If the rating is 1 then the scores become 1,1,2,2,4,5,5. Median = 2. If the rating is 5, then the scores become 1,2,2,4,5,5,5. Median= 4. Regardless, adding an additional category changes the Median. Select Yes

Appearance: 1,1,3,3,5,5. Median = (3+3)/2 = 3. If the rating s 1, then score is 1,1,1,3,3,5,5. Median = 3. If the rating is 5, then the score is 1,1,3,3,5,5,5. Median = 3. Regardless, the median does not change. Select No

Price is similar to Appearance
GMAT695
For each of Six ready-to-eat food products, the table shows a particular product tester’s ratings—ranging from strongly negative (1) to strongly positive (5)—in each of three categories.

ProductFlavorAppearancePrice
A435
B115
C531
D554
E214
F251

Suppose that this product tester was to give ratings for a seventh ready-to-eat food product. For each of the following categories, select Yes if the addition of the ratings for the seventh product could change the median rating in that category. Otherwise, select No.

Attachment:
GMAT-Club-Forum-1k7n3ocl.png
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No. Still 4.

The entries are 1, 1, 4, 4, 5, 5, 5.
4 is the central item in the list (number of items in latest list = 7).

You might have forgotten that the count of list is increased by 1. :)
Azeem123
in price- if the rating is 5 then the median would be 4+5/2=4.5, then why no?
Shafkat26
Flavor: 1,2,2,4,5,5. Median = (2+4)/2 = 3
If the rating is 1 then the scores become 1,1,2,2,4,5,5. Median = 2. If the rating is 5, then the scores become 1,2,2,4,5,5,5. Median= 4. Regardless, adding an additional category changes the Median. Select Yes

Appearance: 1,1,3,3,5,5. Median = (3+3)/2 = 3. If the rating s 1, then score is 1,1,1,3,3,5,5. Median = 3. If the rating is 5, then the score is 1,1,3,3,5,5,5. Median = 3. Regardless, the median does not change. Select No

Price is similar to Appearance
GMAT695
For each of Six ready-to-eat food products, the table shows a particular product tester’s ratings—ranging from strongly negative (1) to strongly positive (5)—in each of three categories.

ProductFlavorAppearancePrice
A435
B115
C531
D554
E214
F251

Suppose that this product tester was to give ratings for a seventh ready-to-eat food product. For each of the following categories, select Yes if the addition of the ratings for the seventh product could change the median rating in that category. Otherwise, select No.

Attachment:
GMAT-Club-Forum-1k7n3ocl.png
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