# Standard Deviation from Percentiles and Mean

#### rpmc

##### New Member
Hello to all and thank you in advance for the help with this.

I am working with a lognormal distribution and am given Percentiles - P10, P50, P90, and Mean.

Question - how do I compute Standard Deviation given these values?

#### vinux

##### Dark Knight
it is easy.. there is only two parameters in the lognormal.. u and sigma

mean = exp( u +sigma^2/2 )
meadian =p50 = exp( u )

now calculate sd.( fist calculate sigma and then sd)

#### rpmc

##### New Member
Apologies for the belated thank you. I appreciate your help!

#### rpmc

##### New Member
A follow-up question. If the distribution is Normal, and I am given Percentiles P10, P50, and P90, what is the formula for Standard Deviation?

Thank you again.

Robert

#### vinux

##### Dark Knight
P50 will be the mean

First calculate k....
Calculate P(Z <k) =0.90 ---(1)
where Z follows Standard Normal distribution.
you will get k as 1.28 ( check again)

Now you know P90 , say q
ie P(X<q) =.90 where X follows Normal distribution with mean (P50) and sd( we have to calculate now).

P( (X-mean)/sd <(q-mean)/sd) =0.90 -----(2)

using 1 and 2
k = (q-mean)/sd solve sd now...