# Standard deviation

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Standard deviation
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Ontologies: MeSH NeuroLex Wikidata Wikipedia

Standard deviation

To aggregate two standard deviation with equal weight one should also use the correlation coefficient between the two random variables. When, e.g., aggregating standard deviation for left and right brain volumes the standard deviation for the total brain volume will be:[1]

$\sigma_T = \sqrt{\sigma_L^2 + \sigma^2_R + 2\sigma_L\sigma_R\rho_{LR}}$

For human brain volume studies the unknown $\rho_{LR}$ have been set to 0.78 based on an independent study.[2] If $\sigma_L = \sigma_R = 1, \rho_{LR}=0.78$

$\sigma_T = \sqrt{1+1+2 \times 0.78} \approx 1.89$