In Country X, a building is in Category A if it has a roof height of

Question

https://gmatclub.com/forum/download/file.php?id=81440 In Country X, a building is in Category A if it has a roof height of at least 350 meters. In the graph, each of the 22 Category A buildings is represented by two points arranged vertically: one representing the comparison of the height of the building’s roof to the number of floors (red circles), the other representing the comparison of the height of the building’s roof to the mean height per floor (black squares). Based on the given information, use the drop-down menus to most accurately complete the following statements about Category A buildings in Country X. The building with the greatest mean height per floor has a roof height between GRAPH_1_PLACEHOLDER meters. There is a GRAPH_2_PLACEHOLDER correlation between the number of floors and the mean height per floor. ID: 100408 1.jpg GMAT-Club-Forum-b3ocy25y.png

Sajjad1994 · Accepted Answer

Official Explanation

The building with the greatest mean height per floor has a roof height between___________meters.

The building with the greatest mean height per floor is represented by the uppermost black square on the graph. The horizontal coordinate of this square indicates that the roof height of the building is between 350 and 370 meters.

The correct answer is 350 and 370.

There is a____________correlation between the number of floors and the mean height per floor.

Where the red circles are in the upper portions of the graph, the corresponding black squares are generally in the lower regions. Similarly, where the red circles are in the lower portions of the graph, the corresponding black squares are generally in the upper regions. This demonstrates a strong negative correlation between the variable represented by the vertical coordinates of the red circles and the variable represented by the vertical coordinates of the black squares. Thus there is a strong negative correlation between the number of floors and the mean height per floor.

The correct answer is strong negative.

Isa1989 · Answer

The first blank is relatively easy to answer, the topmost black square lies between the points 350 and 370 on the axis representing heights of roofs.

For the second blank, one could eyeball the graph to see that as the red circles increase in height, the black squares start to descend so a strong negative correlation between the two.

Hope this helps.

jaykayes · Answer

Here's another way to think about the second part of this question:

Take an example of a building with any roof height, let’s say 400 metres.

If the number of floors (black dot) is let’s say 80, then the mean height per floor (red dot) will be simply 400 divided by 80 = 5 metres.

If the number of floors (black dot) is let’s say 50, then the mean height per floor (red dot) will be simply 400 divided by 50 = 8 metres.

So it’s quite clear that there is a very sharp and clear inverse relationship between the black dos and the red dots, i.e., a strong negative correlation.

DhruvBadaya · Answer

To answer the first blank: The building with the greatest mean height per floor is represented by the uppermost black square on the graph. The horizontal coordinate of this square indicates that the roof height of the building is between 350 and 370 meters.

To answer the second blank: Now, this is relatively hard to answer. But we know what average is. It's the height of the net building divided by total number of floors. Isn't it? From the formula itself, we can determine that there is a negative correlation between number of floors and height of the building.

idao · Answer

We can see there is a positive correlation between the number of floors and height of the building’s roof, and there is a negative correlation between height of the building’s roof and the mean height per floor. Can I say it's a negative relationship between the number of floors and the mean height per floor?

Gemmie · Answer

1. The building with the greatest mean height per floor has a roof height between [350 and 370] meters.

2. There is a [Strong Negative] correlation between the number of floors and the mean height per floor.

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Rex885 · Answer

Hi I have a quick question, I read somewhere that we remove outliers from the data and then compare correlation. If we remove the two black dots in top left of the graph. there seems to be no correlation b/w # of floors and mean hight per floor.
So should we remove the outliers or not?

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Aalto700 · Answer

Can you define or clarify  strong  correlation?  chetan2u   Bunuel   Bismuth83

In this question, I chose Negative, instead of strong negative, and I got 1 question wrong.

samarpan.g28 · Answer

Hi, the options provided are Strong Positive, Negligible, and Strong Negative. Do you mean Negligible?

FrozenDragon · Answer

Most probably You have chosen 'negligible' as your answer. You may have got confused and that's normal. Negligible means no correlation, which suggests that there is no relationship between two variables.

the difference between strong negative and negative correlation is   A  negative correlation  indicates two variables move in opposite directions—as one increases, the other decreases. A  strong negative correlation  simply means this inverse relationship is highly consistent and predictable, with data points tightly clustering together on a scatter plot

FrozenDragon · Answer

it's standard practice to remove outliers, however on Gmat correlation is more about general trend, not strict mathematical rules.

if 1 or 2 outliers shows you different picture than general trend then you can ignore it. However if it supports general trend then no need to overthink about it.

gamebird96 · Answer

Small doubt here, we can see that there is strong co-relation b/w height and #floors.. so mathematically we can say #floor is proportional to height... doesn't that mean (height/#floor) is sort of constant, and now if you plot (height/#floor) vs #floor it should be constant and correlation should be negligible?

Bunuel · Answer

There is a strong negative correlation between the number of floors and the mean height per floor because buildings with more floors generally have a lower mean height per floor.

Proportionality means that the ratio of roof height to the number of floors is constant. If roof height were proportional to the number of floors, the mean height per floor would remain constant, and the correlation would be negligible. Here, that ratio is  not  constant, it generally decreases as the number of floors increases.

In Country X, a building is in Category A if it has a roof height of

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In Country X, a building is in Category A if it has a roof height of

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