Mathematics · essential
Effect of origin and scale on variance and standard deviation for JEE
Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data
Formula
If \(y=\frac{x-a}{h}\), then \(\sigma_y^2=\frac{\sigma_x^2}{h^2}\), \(\sigma_y=\frac{\sigma_x}{|h|}\); equivalently, if \(y=ax+b\), then \(\sigma_y^2=a^2\sigma_x^2\), \(\sigma_y=|a|\sigma_x\).
Variables: \(a,b,h\): constants, \(\sigma_x,\sigma_y\): standard deviations.
Conditions: Change of origin does not affect variance or standard deviation; change of scale does.
Coding transformations and comparison problems.