I Need help simplifying standard error formula for redshift

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The discussion focuses on simplifying the standard error formula for redshift, denoted as sigma(z). Key components include standard error (SE), the number of observations (n), standard deviation (sigma), total population (N), and population mean (mu). The original equation was deemed overly complex, prompting a request for simplification. Corrections were made regarding the introduction of a square root and the use of a biased formula for standard deviation, which may affect results based on the size of N. The conversation emphasizes the importance of clarity in statistical formulas for accurate calculations in astrophysics.
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Filled in all the equations for standard error in redshift (standard error formula, standard deviation formula, mean formula), would like to simplify it, too complicated otherwise thanks in advance :)
Schermafbeelding 2024-04-27 123159.png

SE = standard error, expressed as sigma(x)
n = number of observations we take into account (from a total population) when calculating the standard error
sigma-index-x = standard deviation
N = total population
x-index-i = element of that population
mu = mean of the population
-> filled in all the equations and replaced x by z (redshift) to determine the standard error in z (sigma(z))
-> as you can see, last equation is way too complicated, can anyone help me simplify it?
PS. In the finale expression, x-index-i should be substituted with z-index-i
 
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Where you substituted your third expression into your second, why did you introduce a square root?
 
Small mistake of mine, I corrected it, thank you for your sharp eye!
 
Right. And what's left is a textbook formula for standard deviation, although you are using the biased formula. Whether that matters or not depends on the size of your ##N##.
 
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