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I don't understand how astronomers estimate the redsfhit of a cluster. As far as I understand a cluster of galaxies is something really "big", so I expect that different galaxies in the cluster have different redshifts.

The redshift of the cluster is some average of the redshift of every galaxy in the cluster?

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Yes, it is the average redshift of galaxies that belong to a cluster.

There is of course an uncertainty in that, but a typical velocity dispersion among galaxies in a massive galaxy cluster is 1000 km/s. So the redshift error due to the uncertainty in the mean is $$\Delta z \sim \frac{\Delta v}{c} = \frac{\sigma_v}{c\sqrt{n}}= \frac{0.0033}{\sqrt{n}},$$ where $n$ is the number of galaxies in the cluster with a measured redshift.

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  • $\begingroup$ I can't see why $0.0033$ appears in your equation. $\endgroup$ – Nothing Jun 24 at 22:16
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    $\begingroup$ $\Delta z\sim \Delta v/c$ $\endgroup$ – Rob Jeffries Jun 24 at 22:35

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