APFIVE Effects of Linear Transformations on Summary Statistics
A dataset of six employee salaries is given as $3000, $7000, $15000, $22000, $23000, and $38000. Consider two transformations of this data: adding a constant of $3000 to each salary, and multiplying each salary by 1.10 to reflect a 10% raise. All of the following statements about the effects of these transformations are true EXCEPT:
A
A 10% raise multiplies the mean salary by 1.10.
B
Adding a constant to every salary increases the mean by exactly that constant.
C
Adding a $3000 constant to each salary results in the mean being multiplied by $3000.
D
While adding the same constant does not change the differences between salaries, multiplying each salary by 1.10 scales both the mean and the spread by 10%.
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