average product of 2 deviations — stdev, correlation..

This is the basis of standard deviation, correlation coefficient and variance.

Say we have 22 measurements of student heights. First we find the mean. Deviation is defined as a “distance” from the mean.

Variance is the simplest idea — average product of deviation*deviation. It has dimension of meter*meter

Standard deviation σ is based on variance — √average product of deviation *deviation. Dimension of meter

Now we pair up student’s height deviation and the same student’s weight deviation.

Correlation coefficient is — (average product of deviationh * deviationw) /(σh * σw) Dimension of …nothing.

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