How Does a Linear Transformation Affect Statistical Measures?

[Ezekiel20]

Help please??

To anybody that can offer a hand.


<x>=5, Standard Deviation = 2, median Mx=4.5, Quartile1=4, Quartile 2=6, xmin=0, xmax=9.

After a linear tranform: y= -2x+1. What are <y>, Standard deviation y, median y, Q1y, Q2y, Ymin, Ymax.

I was given this equation for homework and I am totally lost.

 

[mathman]

Except for the standard deviation, all the items you want can be botained by simply applying the linear transformation to an x quantity to get the corresponding y quantity. For example <y>=-2<x>+1. To get the standard deviation, you multiply by the absolute value of the multiplicative constant, therefore y standard deviation is 4.

 

[matt grime]

Originally posted by Ezekiel20
To anybody that can offer a hand.


<x>=5, Standard Deviation = 2, median Mx=4.5, Quartile1=4, Quartile 2=6, xmin=0, xmax=9.

After a linear tranform: y= -2x+1. What are <y>, Standard deviation y, median y, Q1y, Q2y, Ymin, Ymax.

I was given this equation for homework and I am totally lost.

you know how you've got all the formulae for workingout those quantities? we,, instead of putting an x in the, try putting ax+b and seeing what the answer is and how it relates to the untransformed quantity:

mean: E:=\sum_nx_i/N where N is the number of measurements (or whatever) transform by ax+b \sum_n(ax_i+b)/N=a\sum_nx_i/N +\sum_nb/N = b+ a\sum_nx_i/N = b+aE