Students in a large psychology class measured the time, in seconds, it took each of them to perform a certain task. The times were later converted to minutes. If a student had a standardized score of \(z=1.72\) before the conversion, what is the standardized score for the student after the conversion?

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Changing the units will not change the \(z\)-score. The relationship between each value relative to the mean will stay the same.

We can also see this from the equation for the standard score:

$$ Z = \frac{x-\mu}{\sigma} $$

Changing the units from seconds to minutes would be the same as dividing each value by 60.

$$ Z = \frac{\frac{x}{60}-\frac{\mu}{60}}{\frac{\sigma}{60}} $$ $$ Z = \frac{\frac{x-\mu}{\cancel{60}}}{\frac{\sigma}{\cancel{60}}} $$ $$ Z = \frac{x-\mu}{\sigma} $$