Effects of Linear Transformations

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Prerequisites

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.

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