# [BiO BB] Mean and Standard deviation

Frenz, Christopher CHRISTOPHER_FRENZ at NYMC.EDU
Tue Feb 21 12:40:37 EST 2006

Oops!  Missed the fact that he posted the SD values, so I didn't note the direction of the change.  Let's give a full explanation this time.

SD= sqrt(Summation((Xi-Mean)^2)/(n-1)) where Xi is used to iterate through each value in the data set.  Basically you begin by summing the squared differences between the mean and each value in the data set.  Getting rid of the endpoints will likely lessen the value of this number resulting in a smaller SD, since the remaining numbers will result in smaller differences with the mean.  This number is then divided by (n-1), where n is the sample size.  Thus a smaller n will result in a larger SD and a larger n will result in a smaller SD.  The final value of SD is the number square root of the number that results from the division by (n-1).

Chris

-----Original Message-----
From: bio_bulletin_board-bounces+christopher_frenz=nymc.edu at bioinformatics.org on behalf of Subhash Agarwal
Sent: Tue 2/21/2006 12:03 AM
To: bioinformatics.org
Subject: [BiO BB] Mean and Standard deviation

Dear Forum Memebers

I have a dataset with 394 data points. The frequecy distribution of which is as follows:

0-0.02  85    0.02-0.04  63    0.04-0.06  51    0.06-0.08  39    0.08-0.1  36    0.10-0.12  24    -0.12-0.14  21    0.14-0.16  19    0.16-0.18  13    0.18-0.2  10            >0.20            33

The mean and SD of the data is 0.0842 and 0.0853. But when the data points from 0-0.02 and > 0.2 are removed and the mean and SD is calculated it is found that mean doesnt change much (0.0819) but SD does (0.0472). My query is what can I interpret from this regarding the data.

If any of the forum members feels that this question should be addressed to some other place do let me know.

Thanks
Subhash

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