The table lists data on each of 8 items advertised by an Internet reta

Question

The table lists data on each of 8 items advertised by an Internet retailer on a single web page as part of a one-day sale. The term customer refers to anyone who viewed that web page on that day. For each item, the page placement denotes the quadrant of the page on which the item's advertisement appeared; the mean eye time is the average (arithmetic mean) number of seconds that each customer spent viewing the item's advertisement; the info click percentage is the percentage of all customers who clicked a button for more information; and the sales rank is the item's ranking based on sales, where a lesser number denotes greater sales.

For each of the following statements about this data, select Yes if the statement can be inferred from the given information. Otherwise, select No.

Item  
  Page placement  
  Mean eye time
(seconds)  
  Infolclick
percentage (%)  
  Sales rank  
 
   A  
 upper left 
 8.2 
 35 
 2 
 
   B  
 lower right 
 7.15 
 67 
 3 
 
   C  
 lower left 
 7.25 
 22 
 8 
 
   D  
 upper right 
 8.35 
 52 
 1 
 
   E  
 upper left 
 8.42 
 74 
 7 
 
   F  
 upper right 
 7.35 
 18 
 4 
 
   G  
 lower left 
 6.55 
 5 
 6 
 
   H  
 lower right 
 6.87 
 22 
 5

For each of the following statements about this data, select  Yes  if the statement can be inferred from the given information. Otherwise, select  No .

chetan2u · Accepted Answer

For directly proportional values, the increase should correspond to an increase in other value. 
However, positively correlated is the general trend of the values.

MartyMurray · Answer

The table lists data on each of 8 items advertised by an Internet retailer on a single web page as part of a one-day sale. The term customer refers to anyone who viewed that web page on that day. For each item, the page placement denotes the quadrant of the page on which the item's advertisement appeared; the mean eye time is the average (arithmetic mean) number of seconds that each customer spent viewing the item's advertisement; the info click percentage is the percentage of all customers who clicked a button for more information; and the sales rank is the item's ranking based on sales, where a lesser number denotes greater sales.

For each of the following statements about this data, select Yes if the statement can be inferred from the given information. Otherwise, select No.

For each of the following statements about this data, select Yes if the statement can be inferred from the given information. Otherwise, select No.

Infoclick percentage is directly proportional to mean eye time.

When values are "directly proportional," the ratio of the values is constant. In other words, when one value increases or decreases, the other value increases or decreases proportionally. In simple terms, when two numbers are directly proportional, when one increases the other increases as well.

So, it's likely that we can tell whether infoclick percentage is directly proportional to mean eye time by simply checking to see whether the two values increase together.

To do so, we can sort the table on Mean eye time to line up the mean eye time values from least to greatest and then see whether the infoclick values also go from least to greatest.

Doing so, we see that, when Mean Eye Time is sorted from least to greatest, Infoclick percentage is not lined up from least to greatest. For example, in the Infoclick percentage column, 67 comes before four lower values, 22, 18, 35, and 52, and 22 comes before 18.

Select  No .

The 2 items having the greatest sales were advertised in the upper part of the web page.

To find this answer, we can first find the 2 items with the greatest sales by sorting by Sales rank.

We also must note what the text says about sales rank:

the sales rank is the item's ranking based on sales, where a lesser number denotes greater sales

Doing so we see that the items D and A are the items ranked 1 and 2 and therefore are the items having the greatest sales.

Looking in the Page placement column, we see that D is placed upper right and A is placed upper left.

So, these 2 items were advertised in the upper part of the page.

Select  Yes .

Mean eye time was greatest for the item having the greatest infoclick percentage and least for the item having the least infoclick percentage.

To find this answer, we can sort on Infoclick percentage to identify the items with the least and greatest infoclick percentage and then see whether those items are also those with the least and greatest mean eye time respectively.

Sorting on Inforclick percentage, we see that the items with the least and greatest infoclick percentages are G and E.

Then, sorting on Mean eye time, we see that the items with the least and greatest mean eyes times are also G and E.

So, we see that the the items with the greatest and least Infoclick percentages and the items with the greatest and least mean eyes times are the same items.

Select  Yes .

Correct Answer   No, Yes, Yes

JoeAa · Answer

for Q1, if it's said it's proportional would it make more sense? can we pick yes?

MartyMurray · Answer

No, because the ratios of Infoclick percentage to mean eye time vary a lot.

For example, the when mean eye time is 6.87, the ratio of Infoclick percentage to mean eye time is about 3:1. Then, when mean eye time is 8.42, the ratio is about 9:1.

So, we really have no basis for the statement that Infoclick percentage is proportional to mean eye time.

chetan2u · Answer

Proportional   just means a  Ratio . It could be directly or inversely proportional. But in either case, the ratio has to be same.

Here, as  MartyMurray  has also shown, the ratios are different.

anikpait17 · Answer

for the first question, where we discuss on Infoclick % and mean eye time if they are correlated/directly proportional, as the value of infoclick % increases, the mean eye time increases initially, then there are 2-3 values that break the trend at irregular intervals, my question is that we have encountered similar questions where 2-3 values even if they break the trend in irregular intervals, we still say that it is positively correlated, is there some threshold on when we say that its not positive but neutral?

MarendraNodi · Answer

I agree with anikpait17 that we've come across comparable scenarios in which 2-3 data points, despite occasionally diverging from the trend at irregular intervals, are still deemed correlated because their trendline suggests so. The situation here is same; drawing a trendline would portray a positive correlation.

Here are some examples in which even if some data points break, its considered to be correlated:
https://gmatclub.com/forum/in-country-x ... 68356.html
https://gmatclub.com/forum/the-table-su ... 09558.html

MartyMurray Can you please help whats the exact threshold? I have seen similar cases in TTP's example as well.

TargetMBA007 · Answer

Based on the discussion in this question, my understanding is as under
We need to differentiate between "proportion" and "correlation", as a lot of other DI questions focus on "correlation"

Proportional and directly proportional are interchangeable, and imply a strictly linear relationship with no aberrations allowed (i.e. the ratio of change needs to be constant), but "correlation" implies a more flexible relationship, where the trend matters as opposed to the individual entries. Hence if the question, asked if they "are positively correlated" the answer would be yes, but as it states "directly proportional" the answer is no.

MartyMurray   KarishmaB  - would love to know if you agree with this understanding?

Thanks

chetan2u · Answer

Marty and Karishma too will pitch in, but I would just give my two bits as I happen to see the query.

You are ok with your understanding. But just a point
 Directly  p​​​​roportional means the two quantities increase or decrease together in a certain constant ratio. It's equivalent in correlation is  positive  correlation, which tells us that  most  of the data moves in same direction, that is as one increases, the other too increases.

Inversely  p​​​​roportional means the two quantities move in opposite direction in a certain constant ratio. It's equivalent in correlation is  negative  correlation, which tells us that  most  of the data moves in opposite direction, that is as one increases, the other decreases.

adityakaregamba · Answer

KarishmaB  Can you please explain the difference between directly proportional and positively correlated? There are questions where, using the same data points, if the question asked for correlation, it was positively correlated

KarishmaB · Answer

Infoclick percentage is directly proportional to mean eye time. Sort as per mean eye time. Directly proportional means if one doubles, the other doubles too. If one halves, the other halves too. Their ratio remains constant. No such relation exists. ANSWER: No The 2 items having the greatest sales were advertised in the upper part of the web page. Sort as per sales rank. The top two ranks were both in upper part of the page ANSWER: Yes Mean eye time was greatest for the item having the greatest infoclick percentage and least for the item having the least infoclick percentage. Sort as per mean eye time. G has the lowest mean eye time and E has the highest. Sort as per infoclick percentage. G again has the lowest infoclick percentage and E has the highest. ANSWER: Yes Table Analysis discussed here: https://youtu.be/41uPmg6ipos

KarishmaB · Answer

Directly proportional means if one doubles, the other doubles too. If one halves, the other halves too. Their ratio remains constant.

Positive correlation means if one increases the other usually increases too. If one decreases, other usually decreases too. By how much is not known. Positive correlation can take a value anywhere from more than 0 to 1.
A co-efficient of 0.2 indicates a weak correlation and 0.8 indicates a strong correlation.

Gemmie · Answer

1.    Infoclick percentage is directly proportional to mean eye time. => No

To check this, let's look at the infoclick percentage and mean eye time for each item. If the infoclick percentage is directly proportional to mean eye time, items with higher mean eye time should have a higher infoclick percentage and vice versa.

Sort by Eye time (ascending)
Item G: 6.55 seconds, 5% infoclick
Item H: 6.87 seconds, 22% infoclick (+)
Item B: 7.15 seconds, 67% infoclick (+)
Item C: 7.25 seconds, 22% infoclick (-)
Item F: 7.35 seconds, 18% infoclick (-)
Item A: 8.2 seconds, 35% infoclick (+) (but still much lower than B)
Item D: 8.35 seconds, 52% infoclick (+) (but still lower than B)
Item E: 8.42 seconds, 74% infoclick (+)

2. The 2 items having the greatest sales were advertised in the upper part of the web page. => Yes

The items with the greatest sales are those with the lowest sales rank.

Sort by sales rank
Item D: Sales rank 1, upper right
Item A: Sales rank 2, upper left

3. Mean eye time was greatest for the item having the greatest infoclick percentage and least for the item having the least infoclick percentage. => Yes

Sort by Infoclick
+ The item with the greatest infoclick percentage is Item E 
+ The item with the least infoclick percentage is Item G

Sort by eye time
+ Highest for Item E
+ Lowest for Item G

Nitish05 · Answer

What helped me was to flip the question and ask what would the data look like, if infoclick was directly proportional to mean eye time.

If the infoclick percentage were directly proportional to the mean eye time, the ratio between the two values would remain constant. This means that as the mean eye time increases or decreases, the infoclick percentage would increase or decrease in the same proportion.

Let's assume the constant ratio is k. If we take the mean eye time and multiply it by k, we should get the infoclick percentage. For example, if the mean eye time is 6.87 seconds and the infoclick percentage is 22%, the ratio kk would be:
k=22/6.87≈3.2k

Using this ratio, we can calculate the infoclick percentage for other mean eye times. Here are a few examples:
 
 For a mean eye time of 7.15 seconds: Infoclick percentage=7.15×3.2≈22.88  
 
 For a mean eye time of 8.35 seconds: Infoclick percentage=8.35×3.2≈26.72  
 
 For a mean eye time of 8.42 seconds: Infoclick percentage=8.42×3.2≈26.94

In this directly proportional relationship, the infoclick percentage would consistently follow the same ratio relative to the mean eye time.

Now it becomes easier to compare it against the actual data and see that it is, in fact, not following the same trend. Hence a No.

napolean92728 · Answer

That's what it's written proportional here and not correlated, so directly proportional means if one doubles the other should double, if one halves the other should halve too... but it's not happening here so the answer is no

Nsp10 · Answer

Hello,
Thank you for the meaningful conversation regarding Correlation and Proportionality, 
I understood that there is no Proportionality here, 
but can we say it is positive correlated ? {though weak but still positive}

cheshire · Answer

You’re right that it isn’t a perfect proportional relationship, but in generally most of the ads that grabbed people’s attention for longer also tended to rack up higher click-through rates. Even though a couple of items don't follow this trend exactly.

soniasw16 · Answer

So in this case, can we say that info click and mean eye time are  positively correlated?  Since when mean eye time increases, infoclick usually increases too?

egmat · Answer

soniasw16

Let's analyze whether the data shows positive correlation:

When I arrange items by increasing mean eye time:
 
 G:  6.55  seconds →  5\%  infoclick 
 H:  6.87  seconds →  22\%  infoclick  
 B:  7.15  seconds →  67\%  infoclick 
 C:  7.25  seconds →  22\%  infoclick  (drops from B)  
 F:  7.35  seconds →  18\%  infoclick  (drops further)  
 A:  8.2  seconds →  35\%  infoclick  (increases)  
 D:  8.35  seconds →  52\%  infoclick  (increases)  
 E:  8.42  seconds →  74\%  infoclick  (increases)

The verdict:  There's  some  positive correlation, but it's weak and inconsistent. Notice how from B to F, mean eye time increases while infoclick actually decreases (from  67\%  to  18\% ). This breaks the "usually increases" pattern you mentioned.

I hope this clears up your confusion!

The table lists data on each of 8 items advertised by an Internet reta

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Item	Page placement	Mean eye time (seconds)	Infolclick percentage (%)	Sales rank
A	upper left	8.2	35	2
B	lower right	7.15	67	3
C	lower left	7.25	22	8
D	upper right	8.35	52	1
E	upper left	8.42	74	7
F	upper right	7.35	18	4
G	lower left	6.55	5	6
H	lower right	6.87	22	5

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The table lists data on each of 8 items advertised by an Internet reta

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

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