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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.


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

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

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

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.
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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?
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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.­
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This question is very easy, I got it correct in 2:08, which is below average because I only have average intelligence. But though compared to the official problem this is not a good problem.
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This question is very easy, I got it correct in 2:08, which is below average because I only have average intelligence. But though compared to the official problem this is not a good problem.
­cool story bro...
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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
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TargetMBA007
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
­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.
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TargetMBA007
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
­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.
­Thanks for your input Chetan. This is certainly different from my understanding, as I thought with positive correlation, its the trend that matters, and the individual data points, or the "exact degree" of change between the data points can vary, whereas with "direct proportion", the exact degree of change between the data points needs to be consistent. I can certainly be wrong here.

Would love to hear MartyMurray KarishmaB views, as well as more inputs on this. 

 
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That is exactly what I have written. I have elaborated on the the two type of correlations and proportions.

Proportional means varying with a constant ratio, while correlations talk of most data in certain trend.
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That is exactly what I have written. I have elaborated on the the two type of correlations and proportions.

Proportional means varying with a constant ratio, while correlations talk of most data in certain trend.
­
I see your point now Chetan and glad we are on the same page. I think a good clarification to add would be, that "directly proportional" would always be equivalent to "positive correlation", but "positive correlation" would not always be equal to "directly proportional". 
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chetan2u
That is exactly what I have written. I have elaborated on the the two type of correlations and proportions.

Proportional means varying with a constant ratio, while correlations talk of most data in certain trend.
­
I see your point now Chetan and glad we are on the same page. I think a good clarification to add would be, that "directly proportional" would always be equivalent to "positive correlation", but "positive correlation" would not always be equal to "directly proportional". 
Hi

Equivalent here was not to equate directly proportional to positive correlation. What it meant was Directly proportional’s equivalent term in correlation is positive correlation.
It was only equivalent in the direction both data points move.

.

Posted from my mobile device­
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chetan2u
That is exactly what I have written. I have elaborated on the the two type of correlations and proportions.

Proportional means varying with a constant ratio, while correlations talk of most data in certain trend.
­
I see your point now Chetan and glad we are on the same page. I think a good clarification to add would be, that "directly proportional" would always be equivalent to "positive correlation", but "positive correlation" would not always be equal to "directly proportional". 
Hi

Equivalent here was not to equate directly proportional to positive correlation. What it meant was Directly proportional’s equivalent term in correlation is positive correlation.
It was only equivalent in the direction both data points move.

.

Posted from my mobile device­
­Sure, I got that sentiment, but still feel the clarification is still vital, because lets say we were looking at a set of data that was positively correlated with another set of data, we could not describe the set as "proportional", unless the specific condition of the ratio of change in data points being identical was met. However, if we were looking at two "proportional" sets, we could immediately away say that the data is "correlated", making the two terms interchangeable under that specific scenario. 
 
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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
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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.

ItemPage placementMean eye time
(seconds)
Infolclick
percentage (%)
Sales rank
Aupper left8.2352
Blower right7.15673
Clower left7.25228
Dupper right8.35521
Eupper left8.42747
Fupper right7.35184
Glower left6.5556
Hlower right6.87225
(Sort ↕ the table by clicking on the headers)

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.

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: YesTable Analysis discussed here:
https://youtu.be/41uPmg6ipos­
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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
­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.
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