A perfect positive correlation is given the value of 1. A perfect negative correlation is given the value of -1. If there is absolutely no correlation present the value given is O. The closer the number is to 1 or -1, the stronger the correlation, or the stronger the relationship between the variables. The closer the number is to 0, the weaker the correlation. So something that seems to kind of correlate in a positive direction might have a value of 0.67, whereas something with an extremely weak negative correlation might have the value -.21.
An example of a situation where you might find a perfect positive correlation would be when every time that "x" number of people go, "y" amount of money is spent on tickets without variation.
An example of a situation where you might find a perfect negative correlation would be if with every increase in X, same amount of y decreases.
On the other hand, a situation where you might find a strong but not perfect positive correlation would be if you examined the number of hours students spent studying for an exam versus the grade received. This won't be a perfect correlation because two people could spend the same amount of time studying and get different grades. But in general the rule will hold true that as the amount of time studying increases so does the grade received.

Degree of correlation measures the extent to which items are correlated. Nearer is the value of r to 1 higher is the degree of correlation, nearer is the value of r to zero, closer is the value of r to zero. Direction is indicated by sign of + or -. A + sign indicates positive correlation-i.e. when x increases, y increases and vice verca and a - sign shows negative correlation i.e. when x increases, y decreases and vice versa.

Through the coefficientof correlation, we can measure the degree or extent of the correlation between two variables. On the basis of the coefficient of correlation we can also determine whether the correlation is positive or negative and also its degree or extent.
Perfect correlation: If two variables changes in the same direction and in the same proportion, the correlation between the two is perfect positive. According to Karl Pearson the coefficient of correlation in this case is +1. On the other hand if the variables change in the opposite direction and in the same proportion, the correlation is perfect . negative. its coefficient of correlation is -1. In practice we rarely come across these types of correlations.
Absence of correlation: If two series of two variables exhibit no relations between them or change in variable does not lead to a change in the other variable, then we can firmly say that there is no correlation or absurd correlation between the two variables. In such a case the coefficient of correlation is O.
Limited degrees of correlation: If two variables are not perfectly correlated or is there a perfect absence of correlation, then we term the correlation as Limited correlation. It may be positive, negative or zero but lies with the limits ± l. High degree, moderate degree or low degree are the three categories of this kind of correlation. The following table reveals the effect ( or degree) of coefficient or correlation.

Difference between correlation and causation is given below:
1. Definition: "Correlation is a statistical measure (expressed as a number) that describes the size and direction of a relationship between two or more variables. A correlation between variables, however, does not automatically mean that the change in one variable is the cause of the change in the values of the other variable". "Causation indicates that one event is the result of the occurrence of the other event; i.e. there is a causal relationship between the two events. This is also referred to as cause and effect
2. Mutual dependence: Theoretically, the difference between the two types of relationships are easy to identify - an action or occurrence can cause another (e.g. smoking causes an increase in the risk of developing lung cancer), or it can correlate with another (e.g. smoking is correlated with alcoholism, but it does not cause alcoholism). In practice, however, it remains difficult to dearly establish cause and effect, compared with establishing correlation.
3. Pure Chance: The correlation between the two variables may be due to pure chance or co-incidence. But in causation, it is not coincidental but logical.

Correlation is a statistical technique that can show whether and how strongly pairs of variables are related. For example, height and weight are related; taller people tend to be heavier than shorter people. The relationship isn't perfect. People of the same. height vary in weight, and you can easily think of two people you know where the shorter one is heavier than the taller one. Nonetheless, the average weight of people 5'5" is less than the average weight of people 5'6", and their average weight is less than that of people 5'7",etc. Correlation can tell you just how much of the variation in peoples' weights is related to their heights.
(a) Correlation is very helpful when we want to study relationship between two or more variables. (b) Correlation also helps in finding if one variable is dependent on other or not.
(c) When two variables are correlated then the value of one variable can be estimated given the value of other variable using regression equations.
(d) It helps in taking important decisions to a business man, government and sociologists.

 r = \(\frac { n(\sum xy)-(\sum x)(\sum y) }{ \sqrt { n(\sum x2-(\sum x)2[n\sum y2-(\sum y)2] } } \)
r = \(\frac { 6(0)-(-2)\times (28) }{ \sqrt { 6(28)-({ -2) }^{ 2 }(6(196)-{ (28) }^{ 2 } } } \)
r = \(\frac { -56 }{ \sqrt { 52\times 392 } } \)
r = \(\frac { -56 }{ \sqrt { 20384 } } \)