Negative Standard Deviations?

[PMK]

I have a spreadsheet with 52 data points on which I'm trying to identify a +1
standard deviation and a -1 standard deviation. When I use the Excel 2003
std dev function to calculate the info, I get a negative standard deviation
on the -1 calculation. Not being a stats wizard, I think it's mathematically
impossible for a standard deviation to be negative. I am assuming I have a
error in my data or formula. My data has a wide variation from a few around
1500 to many 0 and some data in between. Any thoughts would be greatly
appreciated.

 

[Jim Thomlinson]

StdDev is a measurement of the variablility of the data so you are correct in
assuming that there is no such thing as a negative StdDev. At 1 stddev about
2/3 of your data points will lie within 1 std dev of the average. 2 std dev
is around 95% of the data points. So the avearge temperature in January is 5
degrees +/- 3 degrees 67% of the time means that the temp is going to be
between 2 and 8 degrees most days. I would never calculate the -std dev as it
will be the same as the positive. Not sure if that makes sense...

Post your data pints and your formulas if you are still having trouble...

 

[Gary''s Student]

stdev is always positive. However:

mean+stdev
and
mean-stdev

may be negative if the mean is small or negative.

 

[Joe User]

At 1 stddev about 2/3 of your data points will lie within 1 std dev of
the average.

That is the expected result for a normal distribution. It may or may not be
true for other distributions. As you say, the standard deviation is a
measure of variability from the mean. Its use is not limited to normal
distributions.


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