positive co-relation ? how to see it from the table

[vikram4689]

with the increase in public museums, no. of visitors sometimes increase and sometimes decrease. how can i conclude that both of them are POSITIVELY co-related



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[RonPurewal]

in problems like this one, the point is to identify general trends, not to complete an exhaustive review of every single data point.

while it's true that the correlation between the number of public museums and the number of visitors is not perfect, it should nonetheless be obvious that there is, in general, an increasing trend in the numbers.
in fact, this is the whole point of defining the concept of "correlation" in the first place -- to account for phenomena in which a clear increasing or decreasing trend is present, despite the fact that the correlation is not 100% perfect.

as an analogy, if someone takes eight practice gmat tests and gets the following scores, in order --
520, 510, 570, 560, 600, 610, 660, 640
-- then it should be obvious that there is an overall trend of improvement, even though there is not an increase in every consecutive pair of scores.