To calculate the standard deviation of those numbers:

Correlation measures linearity between X and Y. If ρ(X,Y) = 0 we say that X and Y are “uncorrelated.” If two variables are independent, then their correlation will be 0. However, like with covariance. A correlation of 0 does not imply independence.

Variance is calculated by taking the differences between each number in a data set and the mean, squaring those differences to give them positive value, and dividing the sum of the resulting squares by the number of values in the set.

1. Work out the Mean (the simple average of the numbers)
2. Then for each number: subtract the Mean and square the result.
3. Then work out the mean of those squared differences.
4. Take the square root of that and we are done!

Among these, the first method, i.e. scatter diagram method is based on the study of graphs while the rest is mathematical methods that use formulae to calculate the degree of correlation between the variables.

Graphic Method: This is an extension of linear graphs. In this case two or more variables are plotted on graph paper. If the curves move in same direction the correlation is positive and if moves in opposite direction then correlation is negative. But if there is no definite direction, there is absence of correlation.

To determine the linearity and non-linearity among the variables and the extent to which these are correlated, following are the important methods used to ascertain these: Scatter Diagram Method. Karl Pearson’s Coefficient of Correlation. Spearman’s Rank Correlation Coefficient; and.

It is one of three most potent and extensively used methods to measure the level of correlation, besides the Scatter Diagram and Spearman’s Rank Correlation. The Karl Pearson correlation coefficient method, is quantitative and offers numerical value to establish the intensity of the linear relationship between X and Y.

The Pearson correlation coefficient (named for Karl Pearson) can be used to summarize the strength of the linear relationship between two data samples. The Pearson’s correlation coefficient is calculated as the covariance of the two variables divided by the product of the standard deviation of each data sample.

Step 1: Subtract the median from the mean: 70.5 – 80 = -9.5. Step 2: Divide by the standard deviation: -28.5 / 19.33 = -1.47. Caution: Pearson’s first coefficient of skewness uses the mode. Therefore, if the mode is made up of too few pieces of data it won’t be a stable measure of central tendency.

Correlation analysis, and the Karl Pearson Correlation method, can be used to identify negative, positive and neutral correlations between two data points, e.g., the relationship between the age of a consumer and the color of shirt they might purchase or the level of education of a consumer and the delivery mechanism …