Calculate standard deviation

[Tom Salvitti]

if I have the confidence interval of an average, the sample size, the average is it possible to go back to the standard deviation of the average? FOR INSTANCE IN THIS EXAMPLE mean= 87.9 (83.8-92.0) n = 150
how do you get the standard deviation?

Thanks to everybody

[Roman Mostazir]

It is possible to go backwards and derive the SD but the original distribution from where the parameters are derived may be different. From your information:

87.9 + 1.96s.e. = 92 (upper limit of 95% CI)
s.e. = (92-87.9) / 1.96 = 2.09 (1 standard error)

s.e = sd/sqrt(n)
sd = se*sqrt(n)
sd = 2.09*sqrt(150) = 25.60

[Tom Salvitti]

Thank you!!