I15-13

Question

The table below summarizes information in several categories about the different flights at a major international airport.
      Year   Destination   Charter   Cargo   Commuter   Non-Revenue   Total       2005   Domestic   204   8,193   59,973   1,728   230,242       2005   International   1,266   14,380   5,209   1,324   119,706       2006   Domestic   217   7,419   64,971   1,180   250,413       2006   International   1,023   13,417   5,814   1,269   128,014       2007   Domestic   215   7,586   91,600   1,297   302,958       2007   International   1,823   13,311   6,231   1,198   140,796       2008   Domestic   50   6,820   83,428   1,605   288,025       2008   International   488   10,926   7,964   1,203   150,366       2009   Domestic   30   5,723   81,302   1,398   272,804       2009   International   171   7,839   7,503   525   142,482       2010   Domestic   39   5,942   68,726   1,184   252,445       2010   International   188   9,387   7,714   526   144,525

For each of the following statements, select  True  if the statement can be verified as true based on the information provided. Otherwise, select  False .

Bunuel · Accepted Answer

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Bunuel · Answer

Official Solution:

Statement 1: 
 
Two data sets are positively correlated if they both tend to be higher in the same cases. They are negatively correlated if one tends to be higher in cases where the other is lower. For positively correlated data, their lines tend to slope up or down together; the more consistently this happens, the stronger the positive correlation. Conversely, when two data sets are negatively correlated, the line for one tends to slope up while the other slopes down, and vice versa. The more consistently these opposite slopes occur, the stronger the negative correlation.
 
Sorting the table by Domestic Commuter Flights and Total Domestic Flights reveals a consistent increase in both metrics each year. This indicates a strong positive correlation between Domestic Commuter Flights and Total Domestic Flights.
 
 Statement 2: 
 
By examining Total Domestic Flights, we find that its median is approximately 260,000 flights (calculated as the average of the 3rd and 4th highest figures for Total Domestic Flights). Similarly, the median of Total International Flights is approximately 140,000 flights (calculated as the average of the 3rd and 4th highest figures for Total International Flights). As shown, the median of Total Domestic Flights (260,000) is less than twice the median of Total International Flights (140,000).
 
 Statement 3: 
 
Sorting by Non-Revenue Flights, we can calculate the range as 1,728 - 525 = 1,203. Similarly, sorting by Charter Flights, the range is 1,823 - 30 = 1,793. Therefore, this statement is false.

Correct answer:

There is a strong positive correlation between Domestic Commuter Flights and Total Domestic Flights.  "Yes"

The median of total domestic flights is less than twice the median of total international flights.  "Yes"

The range of non-revenue flights is greater than the range of charter flights.  "No"

Bunuel · Answer

I have revised the question, solution, and formatting by adding more details to enhance clarity

SatyeshRicky · Answer

How to tackle the processing time for these questions? I want to improve speed in DI section. Any tips ?

pwt12 · Answer

I don’t quite agree with the solution. In statements 2 the question is "...total DOMESTIC flights LESS ... INTERNATIONAL..." while the answer highlights that domestic flights were more prevalent (260k vs 140k). Probably a typo in the question statement.

Bunuel · Answer

There is no typo here. The statement says  "the median of total domestic flights is less than  twice  the median of total international flights",  it does not mean domestic flights are fewer.

It simply checks whether 260,000 is less than 2 * 140,000 (which is 280,000).

This condition holds true, so the statement is correct.

SamridhiM · Answer

I don’t quite agree with the solution. In statement 1 it says strong positive co-relation> I agree there is a correlation but it is not strong. 
1. when commuter flights jump by 5K, the total flights jump by 20K
2. when commuter flights jump by 4K, the total flights jump by only 2K
3. when commuter flights jump by 3K, the total flights jump by 20K again
4. when commuter flights jump by 2K, the total flights jump by only 15K

Bunuel · Answer

The correlation isn't about perfectly matching amounts but about consistent  direction . In this case, whenever Domestic Commuter Flights go up, Total Domestic Flights go up too. Since this happens every year, the correlation is strong, even if the changes aren't always by the same amount.

navs18 · Answer

I like the solution - it’s helpful.

navs18 · Answer

I like the solution - it’s helpful.

Mahekk · Answer

I did not quite understand the solution. i did not understand how median is calculated in statement 2

Bunuel · Answer

Sorted domestic totals:
230,242, 250,413,  252,445, 272,804,  288,025, 302,958
 Median is (252,445 + 272,804)/2 = 262,624.5

Sorted international totals:
 119,706, 128,014,  140,796, 142,482,  144,525, 150,366
 Median is (140,796 + 142,482)/2 = 141,639

Twice international median is 283,278
 262,624.5 is less than 283,278, so the statement is true.

MehraShubham · Answer

I like the solution - it’s helpful.

JaneSulema · Answer

I like the solution - it’s helpful. 
I like the solution - it’s helpful.

quasivoluptatem · Answer

I don’t quite agree with the solution. As shown, the median of Total Domestic Flights (260,000) is less than twice the median of Total International Flights (140,000).

How is 260,000<140,000 possible?

Bunuel · Answer

260,000 is not less than 140,000. The comparison is 260,000 < 2 * 140,000. So it is 260,000 < 280,000, which is true.

Check the statement:

The median of total domestic flights is less than  twice  the median of total international flights.

I15-13

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My Rewards

Year	Destination	Charter	Cargo	Commuter	Non-Revenue	Total
2005	Domestic	204	8,193	59,973	1,728	230,242
2005	International	1,266	14,380	5,209	1,324	119,706
2006	Domestic	217	7,419	64,971	1,180	250,413
2006	International	1,023	13,417	5,814	1,269	128,014
2007	Domestic	215	7,586	91,600	1,297	302,958
2007	International	1,823	13,311	6,231	1,198	140,796
2008	Domestic	50	6,820	83,428	1,605	288,025
2008	International	488	10,926	7,964	1,203	150,366
2009	Domestic	30	5,723	81,302	1,398	272,804
2009	International	171	7,839	7,503	525	142,482
2010	Domestic	39	5,942	68,726	1,184	252,445
2010	International	188	9,387	7,714	526	144,525