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Our life is full of events and some of these events are related to each other. When we say that the two events are related to each other, we mean that the outcome of a second event depends on the outcome of the first event or vice-versa. For example, your happiness is related to the number of gifts that you receive on your birthday. The more gifts that you receive, the happier you will be. Such events can be regarded are co-related events. However, all the events need not be necessarily related to each other. For example, the marks that you score are not at all related to the amount of amount of rainfall in your area. There may be some other events that may be partially related to each other. The mathematical term ‘Correlation’ is the measure of any pattern between the outcomes of two different events. 

Let us explore what is Correlation in Math

Now that we know that the events can be related to each other, let us find out, what is correlation in Math and how it is calculated. Correlation in mathematics is given by the formula, 

                                                                

The above formula calculates the correlation for two variable x and y that can be regarded as the outcomes of two events. The numerical value of the correlation calculated from the above formulas lies between -1 and +1.  

Now that you know, what is correlation in Math; let us try to find out the significance of the numerical value of correlation and its significance. 
If you will look the mathematical formula for the correlation, you would find that the denominator will always produce real and positive values as we are calculating the root of multiplication of two square values and square values are always positive. The numerator, however, can produce both positive and negative terms as there is no square. A closer look at the numerator will show that it consists of a multiplication of two terms. Thus, if the terms have the same sign (positive or negative); a positive numerator will be obtained. Else, a negative numerator will be obtained if the signs are opposite. To conclude, if the difference of the two qualities with their respective mean values is of opposite sign, we get a positive value of correlation. Else, we get a negative value of correlation.

There are two things to look at the numerical value of correlation. The positive sign indicates that as one quantity increases or decreases, the second quantity also increases or decreases respectively. The magnitude of the correlation indicates the amount of similarity in the rate of their increase of decrease. A perfect +1 correlation is possible only if the two quantities are identical.

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