Finding the mean and standard deviation with only percentile data?

jro

New Member
#1
Assuming the data is normal, how do I find the mean and std deviation? I have the following:

10th percentile - 75,174
25th percentile - 81,627
50th percentile - 89,621
75th percentile - 98,576
90th percentile - 108,463

I can't assume the mean is the 50th percentile right?

I know this should be easy....
 

rogojel

TS Contributor
#2
Actually your data seems to be fairly symmetrically distributed so you could assume that the mean is quite close to the median.
regards
 

Dragan

Super Moderator
#3
Yes, you would use the sample median as the measure of central tendency. In terms of a measure of dispersion, what works best is the inter-decile range i.e., the range between the 10-th percentile and 90-th percentile. Other measures for shape (tantamount to skew and kurtosis) would be the "left-right tail-weight ratio" [ (median - 10-th percentile) / (90-th percentile - median) ] and the "tail-weight factor" [ (75-th percentile - 25-th percentile) / (inter-decile range) ].

See Karian and Dudewicz (Chapter 5, pp. 172-174) for further details in the "Handbook of Fitting Statistical Distributions with R."
 

jro

New Member
#4
Thank you for the reply. So here's my next question: If I do that and calculate the SD using a Z-score and the mean, why am I getting a different SD? I would assume it should be constant... The end goal is to take two other values and determine their Z scores so I can determine their percentile. Thanks!