So, does it suppose anything especially useful around the typical deviation or indicate there are bugs in calculating it, as soon as the figures occupational out prefer the above? The areas are certainly far from being generally spread.

You are watching: Some of the sample values are negative, but can the standard deviation ever be negative?

And as someone stated in one of their responses below, the thing that really surprised me that it just took one SD from the intend for the numbers to go negative and therefore out of the legal domain.

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distributions intend standard-deviation

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edited Nov 22 "11 at 20:46

whuber♦

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asked Nov 18 "11 at 16:12

Andy DentAndy Dent

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There is nopoint that says that the typical deviation has to be much less than or more than the intend. Given a set of data you have the right to save the mean the same yet adjust the standard deviation to an arbitrary degree by adding/subtracting a positive number

*appropriately*.

Using

whuber"s instance dataset from his comment to the question: 2, 2, 2, 202. As stated by

whuber: the intend is 52 and also the typical deviation is 100.

Now, perturb each element of the data as follows: 22, 22, 22, 142. The suppose is still 52 but the traditional deviation is 60.

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edited Nov 18 "11 at 16:50

answered Nov 18 "11 at 16:30

vartyvarty

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Of course, these are independent parameters. You can collection straightforward explorations in R (or another tool you might prefer).

See more: Why Did Some African Nations Transition Smoothly To Independence While Others Experienced Conflict

R> collection.seed(42) # fix RNGR> x mean(x) # and suppose is close to zero<1> -0.0258244R> sd(x) # sd is close to one<1> 1.00252R> sd(x * 100) # range to std.dev of 100<1> 100.252R> Similarly, you *standardize* the information you are looking at by subtracting the intend and dividing by the traditional deviation.

*Edit* And adhering to

whuber"s principle, below is one an infinity of information sets which come close to your four measurements:

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edited Nov 18 "11 at 18:42

answered Nov 18 "11 at 16:30

Dirk EddelbuettelDirk Eddelbuettel

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I am not certain why

Andy is surprised at this outcome, but I know he is not alone. Nor am I sure what the normality of the data hregarding do via the truth that the sd is better than the mean. It is quite easy to geneprice a data collection that is typically dispersed wbelow this is the case; indeed, the standard normal has actually expect of 0, sd of 1. It would certainly be hard to acquire a commonly distribute data set of all positive worths with sd > mean; indeed, it ought not be possible (however it relies on the sample dimension and also what test of normality you use... through a very small sample, odd things happen)

However before, as soon as you remove the stipulation of normality, as

Andy did, there"s no reason why sd should be larger or smaller then the expect, even for all positive values. A single outlier will do this. e.g.