How Does a Linear Transformation Affect Statistical Measures?

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SUMMARY

The discussion focuses on the effects of a linear transformation, specifically the equation y = -2x + 1, on various statistical measures. Given the initial values of x, including a mean of 5, a standard deviation of 2, and quartiles, the transformed mean is calculated as = -2(5) + 1 = -9. The standard deviation of y is determined to be 4, as it is the product of the absolute value of the multiplicative constant and the original standard deviation. The median, quartiles, and range can be derived similarly by applying the transformation directly to the respective x values.

PREREQUISITES
  • Understanding of linear transformations in statistics
  • Familiarity with statistical measures such as mean, median, and standard deviation
  • Knowledge of quartiles and their calculation
  • Basic algebraic manipulation skills
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  • Study the properties of linear transformations in statistics
  • Learn how to calculate transformed statistical measures using different linear equations
  • Explore the implications of transformations on data distributions
  • Practice with additional examples involving linear transformations and their effects on statistical measures
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Ezekiel20
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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.
 
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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.
 


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