Why are units on Mason's SD formula wrong?

[MarkD]

If you look at his formula:

- the average (U) is in $/hr (assuming $ is your monetary measure and hours is your time measurement)
- N is unitless
- X is in dollars
- T is hours

Therefore, simple unit analysis of the formula shows that variance has units of $^2 / hrs, and therefore SD would have units of $ / sqrt(hrs).

We measure our average in terms of $/hr so logically the SD would have the same units, why is this not so? Has to be a reason.