I need to explain why ArcGIS offers the function "standard deviation" when symbolizing rasters with the Stretch method.
The Standard Deviation is a measure of how spread out numbers are and is calculated by the square root of the Variance. The variance in the Squared differences from the mean and the "n" in the ArcGIS Setting refers to the population.
So what is really happening? Is ArcGIS replacing each Height value with a StdDev value calculated by neighbouring "n" pixels? That would mean the colours represent the average "spread" of heights and not the actual height values themselves.
Am I on the right track here?
Best Answer
If your values are Normally distributed then approximately 68%, 95% & 99.7% of the values lie within 1, 2 & 3 Standard Deviations respectively, see here, so if you are stretching your values of the colour map using SD(2) all of the values that are below 2.5% will be black and all over 97.5% will be white, (depending on your colour scale of course) - this will allow you to see the variation of the more common values without being swamped by the absolute max and min.
Say you are looking at a height map that includes structures and you have a single very high chimney and a single vary deep well included in the map, this might lead to a colour step of 50 ft when the rest of your structures are all in this range, SD will clip those two features allowing you to see the variation of the rest.