Finding upper and lower limits of a graph

1. May 13, 2008

Aki

1. The problem statement, all variables and given/known data
This is not really a homework problem, but it looks like a rather easy problem that I can't quite figure out.

So I have a graph like shown in the attachment: a quantity vs time graph with some data points. I had no problem finding the average, but now I want to find both an upper and lower limits that would enclose 80% of the data points (so like what I have drawn in the graph). My question is: how can I do that using a simple program like Excel?

2. Relevant equations
I tried applying Chebycheff's Inequality
http://en.wikipedia.org/wiki/Standard_deviation

For 80% of the data points, I found the number of standard deviations from the average would be SquareRoot 5. So (SquareRoot 5 * Standard Deviation)/2 , and then add and subtract that from the average to find the limits.

3. The attempt at a solution
Chebycheff's Inequality worked for most graphs. However, for some graphs, I would get a negative value for the lower limit and that's not what I want to see.

Thanks for the help!

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• graph.JPG
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Last edited: May 13, 2008
2. May 13, 2008

HallsofIvy

Staff Emeritus
Chebycheff's Inequality will give difference from the mean. Since here the mean is 80 I don't think you are in any danger of getting a negative lower limit!

3. May 13, 2008

Aki

well I just made up that graph. I can't show the data that I'm working with because it's confidential. Anyhow, there are graphs where if I apply the Chebycheff's Inequality, I get a negative value for the lower limit.