For each of the following statements, select True if the statement can

The answers according to me would be, True, False, False.

Statement 1. By the proportion, I believe the question refers to the ratio of 'Museums in Science, History and Archaeology' to the total number. The ratio comes to be: D - 780/1173 ~ 0.66 and F - 498/775 ~ 0.64 (The calc is prity close so I didn't go for an approximations and went for exact values)

Statement 2: The ratio is greatest in B 220:1.
Statement 3: this was confusing since I had no idea regarding 'positive correlation', and simply used the idea of 'number of public museums' being directly proportional to the number of visitors. In that case, clearly, the increase in the number of public museums does not ensure increase in visitors. Hence, I think it might be false. Please verify!

Regards,
Arpan

The proportion of museums in D related to Science, History and Archaeology is greater than the proportion of museums in F devoted to the same
Without calculator - i really cannot tell, the ratios seem almost equal.
The ratio of public museums to private museums is greatest for C
False: B has highest ratio.
There is a positive correlation between the number of public museums and the number of visitors per year.
Flase: compare A and B, there is one order of magintude difference in number of visitors althoug number of puplic museums is only 10% different. Similar story for G and H.

1. The proportion of museums in D related to Science, History and Archaeology is greater than the proportion of museums in F devoted to the same

Without calculator:
D: 780/1173 ~ 750/1150 = 15/23 = 45/69
F: 498/775 ~ 500/775 = 100/155 ~ 100/150 = 2/3 = 26/45

With calculator: (Calculator will be available during exam)
D: 780/1173 = 0.66
F: 498/775 = 0.64

So the statement is true.


2. The ratio of public museums to private museums is greatest for C

From a quick glance, it is visible that highest ratio is with the country B.

So the statement is false.


3. There is a positive correlation between the number of public museums and the number of visitors per year.

To answer this question, we need to sort the data on the column public (GMAT IR section provides teh sorting feature)
After the sorting, the data can be found as follows

Number of public museums -**- Visitors per year
163 -********************************- 2058817
203 -*******************************- 11579900 -**- increase in number of visitors
220 -********************************- 2427703 -**- decrease in number of visitors
615 -*******************************- 10123438 -**- increase in number of visitors
713 -*******************************- 19648000 -**- increase in number of visitors
960 -*******************************- 12627700 -**- decrease in number of visitors
973 -*******************************- 56065370 -**- increase in number of visitors
1053 -******************************- 40469600 -**- decrease in number of visitors

Thus, it is evident that number of public museums does not have positive correlation with number of visitors per year.

So the statement is false.

Excel format of the table attached.

St1: The proportion of museums in D related to Science, History and Archaeology is greater than the proportion of museums in F devoted to the same
% for D = 0.66
% for F = 0.64
TRUE

St2:The ratio of public museums to private museums is greatest for C
Ratio for C = 2.67
Ratio for E is greater than 9
hence C is not the greatest.
FALSE

St3: There is a positive correlation between the number of public museums and the number of visitors per year.
Out of 8 countries, 5 show an increase in visitors with increase in # public museums.
I would take that as a sign of POSITIVE correlation since majority is showing a +ve corr. It is not necessary that each country must show this +ve relationship (at least that's my understanding that if we plot this line on a graph with # public museums on X asis and Visitors per year on Y axis, if the slope is up, that's +ve correlation. A positive correlation can co-exist with some elements in the set that might be negatively correlated).
TRUE

Any expert comments would be much apprciated for the 3rd part.

experts!...pls throw some light on..."positive co relation"


Thnks
A

I'm no expert, but I do pretty well on IR. My understanding of positive correlation is: can you infer from the data that a relatively large value on one axis is likely to correspond to a relatively large value on the other axis?

So in the scope of this question, if I ask you to estimate the visitors per year for:

(1) 300-museum country, and

(2) 800-museum country,

Are you going to guess a larger value for the second option?

Then there's probably a positive correlation. (Of course, this is assuming a strictly increasing/decreasing line/curve of best fit; this is going to get more complicated if the data follows a parabolic trend or something.)

Hope that helps a bit.

Maybe I'm nitpicking but 'related to' and devoted to aren't the same thing.

Related to implies they contain Art, x,y,z etc...i.e. they have stuff related to Art, x,y,z amongst other stuff.

Devoted to means dedicated to i.e. contains only Art,x,y,z.

A is a poorly written question.

Hi KarishmaB Bunuel! Regarding C, why is there a positive correlation? The number are varying up and down....Tks!

Positive correlation means the correlation co-efficient is greater than 0. It is not the same as direct relation (in which a higher value of one must lead to a higher value of another)
This is what the graph of positive correlation looks like:




When x is increasing, y is also increasing generally. But there can be data points where x is higher but y is lower. As long as the trend is upwards, it is a positive correlation.
Notice how it is different from negative correlation and no correlation.
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