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Excel standard deviation

Posted on 2014-04-09
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Experts:

Maybe I need some more coffee this morning... I'd like to get some pointers for assessing quality of some data.   I'll try to keep it simple.

Let's say I have a mean value which ranges (usually) between 1550 and 1650 (unit is not important here).

Also, I have "uncertainty" values (calculated based on partial derivatives) which may range between +/- 6 to 8.

For sake of argument, let's now assume that I have the following data sets:

Scenario 1:
Mean value = 1600
Uncertainty value = +/- 7
Thus, min = 1593 and max 1607

Scenario 2:
Mean value = 1570
Uncertainty value = +/- 8
Thus, min = 1562 and max 1578

Scenario 3:
Mean value = 1650
Uncertainty value = +/- 8
Thus, min = 1642 and max 1658

I'd like to put these values into perspective of "quality" (i.e., comparing the three different scenarios).    Given that I have a fairly consistent range for both mean values and min/max values, the proportional quality (e.g., min/mean or max/mean) may not tell a good "story" when those values will change.

That said, given these aforementioned information, does anyone one of a good way to suggest "quality" of data where slight changes in mean/min/max ranges result in different interpretation(s)?

Ideally, I'd like to plot these data (maybe on normal curve)... I'm open to suggestions though.

I hope this makes sense... again, I'm trying to keep it simple here.

Thanks,
EEH
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Question by:ExpExchHelp
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aburr earned 1500 total points
ID: 39988871
a lot depends on your definition of "quality"
You might try- "  uncertainty divided by mean"      ie     the percent the  uncertainty is of the mean

That will magnify and emphasize the differences in your data sets
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by:ExpExchHelp
ID: 39988904
aburr:

Ok... maybe... current values would be: .44%. .51%, and .48%, respectively.

With respect to a Gaussian (normal) curve, I've looked into suggestion from Mr. Excel.  
https://www.youtube.com/watch?v=_PqnDYMO3lw

How would you go about graphing these values where the mean value is (on average) 200 greater than uncertainty value?

Thanks in advance,
EEH
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Expert Comment

by:aburr
ID: 39990649
The ratio between mean value and uncertainty  makes no difference. You can plot a standard bell curve with your mean and uncertainty using the method in the video no matter what the ratio. The curve will look the same (at the appropriate magnification ) no matter what the ratio.
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You can then sum (if you want) the deviations (or square) of your underlying data from that bell curve and identify the "quality" of the data (if you can assign any reasonable meaning to that "quality").
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