+ Reply to Thread
Results 1 to 8 of 8

Thread: Standard Deviation from Percentiles and Mean

  1. #1
    Points: 2,460, Level: 30
    Level completed: 7%, Points required for next Level: 140

    Posts
    6
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Standard Deviation from Percentiles and Mean




    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?

  2. #2
    Dark Knight
    Points: 6,762, Level: 54
    Level completed: 6%, Points required for next Level: 188
    vinux's Avatar
    Posts
    2,011
    Thanks
    52
    Thanked 241 Times in 205 Posts
    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)
    In the long run, we're all dead.

  3. #3
    Points: 2,460, Level: 30
    Level completed: 7%, Points required for next Level: 140

    Posts
    6
    Thanks
    0
    Thanked 0 Times in 0 Posts
    Apologies for the belated thank you. I appreciate your help!

  4. #4
    Points: 2,460, Level: 30
    Level completed: 7%, Points required for next Level: 140

    Posts
    6
    Thanks
    0
    Thanked 0 Times in 0 Posts
    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

  5. #5
    Dark Knight
    Points: 6,762, Level: 54
    Level completed: 6%, Points required for next Level: 188
    vinux's Avatar
    Posts
    2,011
    Thanks
    52
    Thanked 241 Times in 205 Posts
    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...
    In the long run, we're all dead.

  6. #6
    Points: 2,460, Level: 30
    Level completed: 7%, Points required for next Level: 140

    Posts
    6
    Thanks
    0
    Thanked 0 Times in 0 Posts
    Thank you again! Your time and advice are really appreciated.

    Robert

  7. #7
    Points: 1,173, Level: 18
    Level completed: 73%, Points required for next Level: 27

    Posts
    1
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Re: Standard Deviation from Percentiles and Mean

    Hello to all,

    Similar question: for a lognormal distribution, P10, P50 and P90 are given. How do you calculate u and sigma?

  8. #8
    TS Contributor
    Points: 7,284, Level: 56
    Level completed: 67%, Points required for next Level: 66

    Location
    MD, USA
    Posts
    465
    Thanks
    8
    Thanked 11 Times in 11 Posts

    Re: Standard Deviation from Percentiles and Mean


    Quote Originally Posted by Helal View Post
    Hello to all,

    Similar question: for a lognormal distribution, P10, P50 and P90 are given. How do you calculate u and sigma?
    Using the CDF from
    http://en.wikipedia.org/wiki/Log-normal_distribution
    Without me stepping through it, you might have to solve simultaneous equations or use iteration.

    This
    http://en.wikipedia.org/wiki/List_of...mic_identities
    may come in handy.

+ Reply to Thread

           




Similar Threads

  1. Replies: 5
    Last Post: 10-28-2010, 06:04 PM
  2. Replies: 1
    Last Post: 10-16-2010, 09:04 AM
  3. Standard error of the sample standard deviation
    By Taqman in forum Statistics
    Replies: 5
    Last Post: 06-10-2010, 08:50 PM
  4. Standard error of the sampling standard deviation
    By Taqman in forum Psychology Statistics
    Replies: 1
    Last Post: 06-09-2010, 10:24 AM
  5. Dummy variables, standard deviation, standard error
    By Fabio Pieri in forum Statistics
    Replies: 1
    Last Post: 02-04-2008, 10:56 AM

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts






Advertise on Talk Stats