5 Select the statement which correctly completes the sentence
“The effect of a transformation is to …”
A stretch the higher values in the data
B maintain the distance between values
C stretch the lower values in the data
D compress the higher values in the data
E reverse the order of the values in the data

Ask by Fleming Crawford. in Australia

Mar 27,2025

Question

5 Select the statement which correctly completes the sentence
“The effect of a transformation is to …”
A stretch the higher values in the data
B maintain the distance between values
C stretch the lower values in the data
D compress the higher values in the data
E reverse the order of the values in the data

Ask by Fleming Crawford. in Australia

Mar 27,2025

UpStudy AI · Accepted Answer

1. A logarithmic transformation converts the data according to $$ y \rightarrow \log y $$.
2. Because the logarithm is a nonlinear function with a decreasing rate of change as $$ y $$ increases, differences between large $$ y $$ values become relatively smaller.
3. Therefore, when applying a $$ \log y $$ transformation, the higher $$ y $$ values are compressed, while the lower $$ y $$ values are stretched.

Thus, the correct completion is:

D compress the higher $$ y $$ values in the data.
The correct statement is D: compress the higher $$ y $$ values in the data.

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