Understanding The Sign Of A Correlation Coefficient: An Example

In many books on Statistics, it is often stated that correlation between two variables X and Y is positive if, as X increases Y also increase. Equivalently, correlation between X and Y is positive, if large values of X most often correspond to the large values of Y and small values X, most often correspond to small values of Y. The correlation is negative if large values of X most often correspond to small values of Y and visa versa. With an example we show that this statement in not always correct. We also give the correct interpretation for the sign of the correlation and its relation to the behavior of the two random variables.