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My question may be expressed with an example I'm most familiar with..

In many ocean science text books, the mean density of the water column is expressed as $${\widehat\rho}=\int^0_{-h}\rho(z)dz$$

How can this be the mean? Surely you need $1/(b-a)$ (i.e. $1/(-h - 0)$) at the beginning of the RHS of the equation? Why don't the text books show it?

Kind regards,

Mark

Mark
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    Think you mean $1/(0-(-h))$, but I tend to agree. Probably it's a matter of conventions/units: if $\rho(z)$ has units of kg/m$^3$ then $\hat{\rho}$ would have units of kg/m^$2$ instead. – Semiclassical Jul 15 '14 at 16:47

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