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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
31% (02:14) correct
69%
(02:37)
wrong
based on 3636
sessions
History
Date
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Not Attempted Yet
For a certain electronics retailer during each of eight days, both of the graphs show the number of televisions sold and the number of extended warranties sold (whether for televisions or for any other products sold at the store). The scatterplot also includes a trendline that shows the correlation between the daily numbers of televisions and warranties sold.
Select from the drop-down menus the options that complete the statement so that it is accurate based on the information provided.
Among the days represented in the graphs, without the data for Day , the daily numbers of televisions and extended warranties sold would .
ID: 700244
i believe there is a error in the answer of this question, Abhivas chetan2u ... if we exclude point 6, the correlation will increase (from 0.047 to 0.213. see table and graph attached), making for instance the selections "Day 6" and "still be positively, though more strongly, correlated" a valid set of answer
Attachments
table2.png [ 20.83 KiB | Viewed 24484 times ]
4d9cfcac-5705-4b31-9ec8-a27c020c0c11.png [ 99.29 KiB | Viewed 24512 times ]
Abhivas
Note that the correlation depicted in the table is not positive correlation. Positive correlation means that if one variable increases, the other increases too and if one decreases, the other decreases too. But what we see is a predominantly negative correlation. When television bar increases/decreases, the warranty bar decreases/increases in most data points. The exception is Day 4 when both decrease together. If I were to remove day 4, the table will depict a negative correlation.
The scatter plot has all the points and the trendline showing positive correlation only because of the first point on the left (circled in Red). This point is the data of Day 4. Remove this point and your trendline changes to the one shown in green. It is negatively correlated. (shown in the attachment)
Hence the ANSWER here will be 'Day 4' and 'No longer positively correlated'.
This question is discussed here on video:
Attachments
Screenshot 2024-03-09 at 2.38.07 PM.png [ 14.92 KiB | Viewed 22096 times ]
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General Discussion
Hi
Now the correlation means the general trend in data. The right graph gives you that line.
Correlation: The line moves upwards as we move from left to right, that is as we increase number of televisions, there is a general tendency of warranties increasing. (in line graph, x increases as y increases)
So, in the second drop-down, you are left with only two options A and D.
Next look at drop down 1.
It talks of three data
4: (15,12.5) - It is the left most point below the line. Just imagine how this point is holding the line in downward position.
The moment you release the line from here, it will move upwards almost in between the next two points to immediate right.
Now, the right edge of the line remains at (30,20), while the left edge moves up to somewhere at (20,22), in middle of next two points.
Thus the slope is (20,22) to (30,20), that is as x increases from 20 to 30, y decreases from 22 to 20.
So, it becomes negatively correlated.
_________________
Now the correlation means the general trend in data. The right graph gives you that line.
Correlation: The line moves upwards as we move from left to right, that is as we increase number of televisions, there is a general tendency of warranties increasing. (in line graph, x increases as y increases)
So, in the second drop-down, you are left with only two options A and D.
Next look at drop down 1.
It talks of three data
4: (15,12.5) - It is the left most point below the line. Just imagine how this point is holding the line in downward position.
The moment you release the line from here, it will move upwards almost in between the next two points to immediate right.
Now, the right edge of the line remains at (30,20), while the left edge moves up to somewhere at (20,22), in middle of next two points.
Thus the slope is (20,22) to (30,20), that is as x increases from 20 to 30, y decreases from 22 to 20.
So, it becomes negatively correlated.
_________________
Posts: 89
Even I agree with mmdfl.
In Data point no 6, number of televisions is more than warranties. This is opposite to all other data points.
Hence if we remove this then the correlation becomes more positive.
But as per GMAC OE , it seems they are more concerned with the OUTLIERS.
GMAT-Club-Forum-othhw71r.png [ 80.55 KiB | Viewed 8575 times ]
In Data point no 6, number of televisions is more than warranties. This is opposite to all other data points.
Hence if we remove this then the correlation becomes more positive.
But as per GMAC OE , it seems they are more concerned with the OUTLIERS.
Attachment:
GMAT-Club-Forum-othhw71r.png [ 80.55 KiB | Viewed 8575 times ]
The scatterplot above shows each data point labeled with the day it represents on the bar graph.
Hope it helps! It helped me relate both graphs...
The scatterplot above shows each data point labeled with the day it represents on the bar graph.
Hope it helps! It helped me relate both graphs...
Posts: 215
KarishmaB
Hi @KarishmaB @chetan2u
I understood why 'Day 4' and 'No longer positively correlated' is the answer but i am confused about why Day 1 and still be positively, though more strongly, correlated will not be the answer.
Below is my understanding:
Because of Day-1 data, graph is going downwards, but if we remove this Day-1 data, we are removing one negative slope and graph will have a positive slope for MOST of days. Please help!!
Attachment:
GMAT-Club-Forum-b5pw9vt7.png [ 18.79 KiB | Viewed 8061 times ]
Attachment:
GMAT-Club-Forum-nrwm4ja2.png [ 19.97 KiB | Viewed 8065 times ]
Quote:
Day 1 doesn't have much impact on the correlation. The number of televisions doesn't change from Day 1 to Day 2 and number of warranties decline very slightly. So this data point doesn't give us much information and removing it won't have much impact. On the other hand, Day 4 is actually opposite of the usual trend and removing it reverses the trend.
Look at the diagram shared by ruis above and find Day 1 on it. If you remove it, can we say that the line must have become steeper? We can't really say. The placement of points is very similar to before.
Removing Day 4 makes a much bigger splash.
Attachment:
GMAT-Club-Forum-sn9milkf.png [ 18.79 KiB | Viewed 7831 times ]
Attachment:
GMAT-Club-Forum-10m9aa88.png [ 19.97 KiB | Viewed 7835 times ]
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KarishmaB
KarishmaB I totally agree with the first part, as according to the approximate coordinates of the trend - line [(17,15) the lower (30,20) the upper] and the 3 days listed d1(15,27) d4(12,15) d6(25,20) we can see that d1 has the smaller deviation (x=2 y=7) and it's excluded, d4 has x=5 y=0 and the d6 is inside (for x) and at the upper limit (for y) so the d4 is the outlier. The scatter plot also points out that 4th day is the only one away from the rest and as a result is the one that affects the most. But for the second part, after also drawing a scatter plot it seems that again the correlation is negative just not so much. Because from day to day when one coordinate for instance decreases (let's say d1 to d2) the other either is the same (d1 to d2) or increases (d3 to d5). Can you help me please on this?
Gmatguy007
By drawing the trendline with a positive slope, they are implying a positive correlation (though a weak positive correlation). We cannot say that the correlation was negative to begin with because of the trendline in the scatter plot and the mix of data in the bar graph.
After you remove day 4, you do get a clear negative correlation in the bar graph and in the scatter plot and that is why we choose "no longer positively correlated." When one increases the other decreases and vice versa. Look at the data from one day to the next day in the bar graph.
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Here is a detailed video solution for this interesting question. See how this question can be solved in the test environment using "Owning the Dataset" approach.
Let us know if you have any questions.
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I'm still not sure why removing point 6 and making the correlation stronger cannot be a correct answer choice here. I computed the Pearson correlation coefficient (PCC) for both conditions (ie., with and without point 6). And the correlation went from weakly positive to moderately positive. In other words, still positive but stronger. I went over my inputs multiple times, and I'm fairly confident of my matplotlib and python skills. Unless I put in the wrong coordinations? It's kind of hard to get the coordinates to a T. These graphs are are bit small and hard to read.
Attachments
di_warranty_matplotlib.png [ 176.62 KiB | Viewed 4977 times ]
Posts: 16
mmdfl
Hi I agree with you and I found the correlation in Gmat is different than in college statistics. Shame on it.
In college we are told that if the coefficient is larger, stronger correlation.
But in GMAT DI, after looking up the DI OG book, the book says ‘The stronger the correlation, the more tightly the dots cluster around the
sloped line. If the dots spread farther away from the sloped line, or cluster around a line with a less consistent slope, the correlation is weaker or non-existent.’
For this question, based on the DI OG definition, I wouldn’t say if we took point 6 away, the points are more clustered around the fitted line. I would rather say if we add one point near the line, the correlation gets stronger.
Hope GMAC can revolutionized their wrong understanding of CORRELATION.
Hi experts KarishmaB Bunuel
Is it fair to say that trend line won't change as it will still be in same direction due to the point day 3 (20,20) which keeps the line towards it and maintains same directionality IF we remove the point day 6 (20,25)?
I made the mistake in statement-1 while attempting but realised later. Please correct me if this is not the right thinking process to eliminate day 6.
_________________
Is it fair to say that trend line won't change as it will still be in same direction due to the point day 3 (20,20) which keeps the line towards it and maintains same directionality IF we remove the point day 6 (20,25)?
I made the mistake in statement-1 while attempting but realised later. Please correct me if this is not the right thinking process to eliminate day 6.
Abhivas
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Nothing is impossible when you have a self-belief
Correlation though a quantitative measure, is purely qualitative for our purposes on GMAT because we do not calculate it. If I remove day 1 or day 6, the direction of the trend line will likely change but how will correlation change, I don't know without calculating it. The slope of the trend line does not give correlation. Higher slope does not mean higher correlation. Correlation tells you how close the points are to the trend line, whatever its slope.
When we remove day 4, the direction of the trend line changes. The correlation turns negative. We still don't know its value but we know that it has become negative. That is why answer is day 4.
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When we remove day 4, the direction of the trend line changes. The correlation turns negative. We still don't know its value but we know that it has become negative. That is why answer is day 4.
agrasan
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