Mean and standard deviation question

[africanspurs]

Quick question

in what situation can it be possible for the standard deviation to actually be BIGGER than the mean of a data set.

 

[Edwards]

It is possible for the standard deviation to be greater than the mean, even if all data points are positive numbers. However, the only way for this to happen is for most, if not all, data points to be at the extremes (with one extreme much greater in magnitude than the other) and nothing near the average. Generally, in a science experiment, it means the orignal data is garbage.

http://answers.yahoo.com/question/index?qid=20081111192809AAcB6mw

A standard deviation much larger than the mean is certainly possible.
It could be, for example, that your data are highly skewed. E.g. take
the simple dataset 42, 50, 55, 999. The outlier makes it very skewed
and the dataset has a mean of 287 but a st.dev of 475.
Standard deviation is a measure of the spread of your data. You can
also calculate skewness (a measure of asymmetry) & kurtosis (measure
of how "peaked" your dataset is). But I suggest first try plotting
your data (e.g. in the form of a histogram) to get a better idea of
its distribution.

https://groups.google.com/group/sci...0d099b57c6b17392/72981d4130f878ba?hl=en&pli=1

 

[WookieD]

Well I'd say Rainfall for April probably managed it as an example?

 

[Sheikh Ma Nuggets]

Well I'd say Rainfall for April probably managed it as an example?

Yep, a good example. Another would be mean wind speed across the southern plains of the USA: usually relatively calm arenas, however prone to extreme spikes when a 300mph tornado rattles through; short-lived extremity, immediately followed by average conditions.

There's also loads in the mathematical modelling of weather, primarily because algorithms will exponentially increase error rates as they are highly sensitive to outliers within the datasets. Therefore, across 50 runs - a statistically sound sample - you'll reach a certain point in time whereby there will be a high degree of variance. In the weather community, this divergence is colloquially known as 'FI' or Fantasy Island, and it's appearance determines the degree of confidence in a signal or pattern which is proposed within the data.

 

[Crawley]

Yep, a good example. Another would be mean wind speed across the southern plains of the USA: usually relatively calm arenas, however prone to extreme spikes when a 300mph tornado rattles through; short-lived extremity, immediately followed by average conditions.

There's also loads in the mathematical modelling of weather, primarily because algorithms will exponentially increase error rates as they are highly sensitive to outliers within the datasets. Therefore, across 50 runs - a statistically sound sample - you'll reach a certain point in time whereby there will be a high degree of variance. In the weather community, this divergence is colloquially known as 'FI' or Fantasy Island, and it's appearance determines the degree of confidence in a signal or pattern which is proposed within the data.

I had beans for tea

 

[NaijaSpurs]

Standard deviation, yeah those were the days, never again

 

[nw7 yid]

e.g. if your data set is:

-1
1
-1
1
-1
1

Then the mean is 0 and the standard deviation will be >0.

 

[Park Lane James]

Standard deviation, yeah those were the days, never again

Tell me about it. I'm having to dip into that area for coursework and project work and I absolutely despise it.

 

[africanspurs]

thanks guys.

i just needed to check my data. you guys were spot on.....most of the data set seemed fairly consistent but there were couple of outliers i missed and one of them was a LARGE negative

cheers guy.

 

[Aldo]

thanks guys.

i just needed to check my data. you guys were spot on.....most of the data set seemed fairly consistent but there were couple of outliers i missed and one of them was a LARGE negative

cheers guy.

I hate it when that happens.