Effects of Linear Transformations


David M. Lane


Linear Transformations

Learning Objectives
  1. Define a linear transformation
  2. Compute the mean of a transformed variable
  3. Compute the variance of a transformed variable

This section covers the effects of linear transformations on measures of central tendency and variability.

If a variable X has a mean of μ, a standard deviation of σ, and a variance of σ2, then a new variable Y created using the linear transformation

Y = bX + A

will have a mean of bμ+A, a standard deviation of bσ, and a variance of b2σ2.

Please answer the questions:
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