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

Can anyone provide complete explanation on answer provided on GMAT club for this question.

Is the positive correlation mean generic?? I see if we go for specific comparison for every year- there are cases of negative relation also.

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

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

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?­

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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. 

Full solution please

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.

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..

How do we know what to ignore and what not to? Specifically by data, we see 2 outliers in a set of 5, how does that conclude positive corelation?

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?

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.

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)

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.