I have the percentiles of 3 values. The percentiles are 5th, 50th and 95th. The values respectively are 340, 365 and 385. How can I find the median and the standard deviation given that data follow a normal distribution?


The 50th percentile is the median.
I used qnorm(0.05) in R to estimate the number of standard deviations the 5th percentile is from the mean, given a normal distribution. It's 1.644854. Good luck!

  • $\begingroup$ can you explain it please with more detail .I am not good at maths at all $\endgroup$ – Manos Xiliadakis Dec 24 '15 at 8:31
  • $\begingroup$ R is software that can be used (among others) statistical analyses. link You could have looked that 1.64 up in a table as well, but I had an R session open anyway :-) saw your edit If 340 is 1.64 sd away from the mean (in the normal distribution very similar to the median), that means: sd = (365 - 340) / 1.644854 = 15.19892. $\endgroup$ – Jasper Dec 24 '15 at 8:32
  • $\begingroup$ yes but you didnt use the 95th percentile .I cant understand your logic :( :( $\endgroup$ – Manos Xiliadakis Dec 24 '15 at 8:39
  • $\begingroup$ Because a normal distribution is symmetrical, the 95th and the 5th percentile should be equally far away from the mean. In your example that's not the case (I'm sorry I missed that). If you were to calculate it from the 95th to the 50th percentile, you would get a slightly different number. Or you could use that the difference of the 95th and 5th percentile is 2*1.644 sd. $\endgroup$ – Jasper Dec 24 '15 at 8:42
  • $\begingroup$ so in this case as you calculated ,the sd =15.19 right? $\endgroup$ – Manos Xiliadakis Dec 24 '15 at 8:46

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