Zero-Mean Data Sets: Removing Trends & Understanding Analysis

[big man]

I'm doing a course in data analysis using IDL and we're doing trend removal.
This is the heading of the section I'm on:

Trend Removal/Zero Mean Data Sets

The exercises are easy to program, but I just need to find something that explains data analysis.

I was hoping to find an explanation of zero-mean data sets because I'm a bit unclear on that. I did find a formula somewhere, but the site didn't look too reliable. The formula was:

zero-mean=(x-mean)/(standard deviation)

Also the question says to eliminate the trend, that is, "find the data set". Now the data that we're analysing is the carbon dioxide readings. I eliminated the sinusoidal trend (period of 12 months), but then it says to: "sum this set to test whether it is approximately zero. Graph your detrended series"

When I sum the set without the sinusoidal trend it obviously doesn't equal zero since the graph will still be plotted around the region of 350 ppm. I don't particularly get this and I really need help. If anyone can make sense out of my explanation I'd appreciate any help or direction to some useful resources that could help me with data analysis.

 

[Cyrus]

I believe a zero mean data set is just that, a set of data where the mean value is zero. The formula you wrote is the z-score, z = \frac{ \bar{x} -\mu }{ \frac{\sigma}{\sqrt{n}}}

where n is the sample size. I think it is saying that if you sum the values after finding all the z-scores, the mean should be centered at zero.