For each year from 2009 through 2013, the table gives the percentage

Question

For each year from 2009 through 2013, the table gives the percentage of participants in a certain pen-pal program who were in each of four age ranges.

Year  6-10  11-15  16-20  21+    2009  14%  47%  31%  8%    2010  12%  45%  30%  13%    2011  11%  42%  32%  15%    2012  9%  38%  35%  18%    2013  4%  39%  37%  20%

For each of the following pairs of age ranges, select  Positively correlated  if the data given for those two age ranges are positively correlated. Otherwise, select  Not positively correlated.

ID: 700262

chetan2u · Accepted Answer

The table gives us the percentage of participants in a certain pen-pal program who were in each of four age ranges for 5 years. The question is related to correlation, an area that is very often seen on DI now. Positive correlation : Maximum entries in two elements being compared move in same direction. Negative correlation : Maximum entries in two elements being compared move in opposite direction. Here, we have 5 entries or 4 gaps, so 3 out of these 4 gaps should be in same direction. (1) 06-10 and 11-15 Sort the table as per 06-10 years, so all 4 gaps increasing. In 11-15, we have 39>>38<<42<<45<<47, three gaps are increasing, so Positively correlated (2) 06-10 and 16-20 Sort the table as per 06-10 years, so all 4 gaps increasing. In 16-20, we have 37>>35>>32>>30<<31, three gaps are decreasing, so Negatively correlated (3) 16-20 and 21+ Sort the table as per 16-20years, so all 4 gaps increasing. In 21+, we have 13>>8<<15<<18<<20, three gaps are increasing, so Positively correlated

rahul_patnaik · Answer

Please find below analysis.

Positive correlation between two object means that when object A increase then object B also increases and vice versa, when object B decrease the object A also should decrease.

In the above question statement.
1. 6-10, 11-15
in this it we arrange the 6-10 age group column in ascending order we can clear see that with the increase in % value there is a increase in the % value for 11-15 age group also (except between 2013 and 2012, which we need to ignore as the general tread of data is increasing for both) You can plot this in a line graph and check, it will be clearly visible that this is a positive correlation.

2. 6-10, 16-20
In this if we arrange the 6-10 age group in ascending order then we can clearly see that there is a negative correlation with 16-20 age group (Except between 2010 and 2009 which we can ignore as the general trend is negative correlated) please plot this in a line graph and you will be able to see the trend correctly.

3. 16-20, 21+
in this it we arrange the 16-20 age group column in ascending order we can clear see that with the increase in % value there is a increase in the % value for 21+ age group also (except between 2010 and 2009, which we need to ignore as the general tread of data is increasing for both) You can plot this in a line graph and check, it will be clearly visible that this is a positive correlation.

SuvidhaAgarwal KishoreSuravarapu msondhi - FYI, please let me know if any doubts.

Happy learning

Edoua · Answer

Classify the data from 2009 to 2013

1- positively correlated

2-Not positively correlated

3- positively correlated

For the 3rd question we have to observe what can be the general trend and not only focus on the first point…..

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whatsarc · Answer

Positive correlation (aka directly related):  If one increases, the other also increases
 Negative correlation (aka inversely related):  If one increases, the other decreases

6–10, 11–15
movement from 4-14%, corresponding movement 39-47%
Both show increasing trend, hence  positive  correlation

6–10, 16-20
movement from 4-14%, corresponding movement 37-31%
One increasing, another decreasing. hence  not positive

16–20, 21+
movement from 37-31%, corresponding movement 20-08%
Both show decreasing trend, hence  positive  correlation

yipmewmew · Answer

KarishmaB  can you please weigh in on the 3rd option? I understand that just one data point is going against the trend but where would we follow this 'rule' of looking at the general trend while determining the correlation? Here's there's just one data point going opposite, what if there were two? What would the ans be then?

KarishmaB · Answer

There is no such rule, but the general trend would be obvious. Otherwise we would get confused whether the data is correlated at all.
There are 4 increases/decreases so  1 change in the opposite direction would be ok. After all, they are not "directly varying". They are positively correlated and the correlation coefficient could be any positive value less than 1 so there is a fair margin. 
But if 2 changes were in same direction and 2 in opposite, then we cannot extablish any correlation between them.

nust2017 · Answer

Hi Karishma. Can you please explain why we we are looking at correlation in part A from 2013-2009? Should it not be from 2009-2013 which clearly shows negative correlation i.e. from 2009-2013, as the percentage in 6-10 increases, the 11-15 age ranges are decreasing.

KarishmaB · Answer

Positive correlation means that when one quantity increases, the other increases too. When one quantity decreases, the other decreases too.
For part A, From 2009 to 2013, values for both ranges are decreasing. So as one is decreasing, other is decreasing too. Hence there is positive correlation between them..

saurvan · Answer

so as per this, what is the permissible amount of outliers that we need to ignore? Lets say in a set of 5, there are two outliers and 3 are in trend. will that count to be in trend?

KarishmaB · Answer

You don't have 2 outliers in a set of 5 here. Both positively correlated series have only 1 outlier. The other 4 are as per trend. 
2 out of 5 becomes debatable. Then I would like to see what their graphs looks like. Small increase/decrease but overall same trend would indicate positive correlation.

Sanjanaad · Answer

Hi Karishma,

To establish a correlation in these questions, is it necessary to sort the data as per the first data set e.g. 6-10 years age group in the first case? Or should we go by the default sorting given (in this case sequence of years)

KarishmaB · Answer

This is time series data so there is a natural sequence to it. Stick to it. If you plot the two data series with time on x axis, the lines should move in a similar manner is all you require for them to have positive correlation. A question on correlation is discussed here: https://youtu.be/Zx-PysHlhGM I have a video and topic discussion on correlation - exactly how it works for time series data and paired data. You can check it out by using the 3 day free trial on my platform.

Batka · Answer

KarishmaB  Hey, Karishma
I understand how you approached this problem (general trend was focused), while Chetan2U paid attention to differences between each year. I did take the same way you took, and I see both of you're experts. But whose strtgy is more correct here? Please clarify. I thought that we need a general trend, which can be seen by looking at the 1st and the last year numbers (if in the 1st year it was 10% and in the last year it was 15%, then there was an in crease), so if this is the case with both age groups, then a positive correlation is chosen.

Thank you

KarishmaB · Answer

There is nothing called "more correct" strategy. There are various strategies people use to evaluate a question based on what works better for them. You use whatever you feel is more intuitive to you - the answer is correct in either case. Also, if looking at a general trend, you cannot focus on only the first and last year numbers - you see whether usually numbers are moving in one direction. Since technically every case with an r > 0 is positive correlation (even if it is low), "no positive correlation" will typically be a case of "negative correlation" on GMAT since we need to get the answer with observation. There won't be any confusion.

elainejames · Answer

Positive/Negative correlation also comes with an anomaly. As long as the majority or overall data points to one direction, it is okay to have one or 2 small deviations

For each year from 2009 through 2013, the table gives the percentage

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Year	6-10	11-15	16-20	21+
2009	14%	47%	31%	8%
2010	12%	45%	30%	13%
2011	11%	42%	32%	15%
2012	9%	38%	35%	18%
2013	4%	39%	37%	20%

Positively correlated	Not positively correlated
		6–10, 11–15
		6–10, 16-20
		16–20, 21+

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For each year from 2009 through 2013, the table gives the percentage

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