How do I 'reverse engineer' the standard deviation?
My problem is fairly concrete and direct.
My company loves to do major business decisions based on many reports available on the media. These reports relates how our products are fairing in comparison to the competitor's offerings.
The latest report had these scores (as percentages):
Input values (%) 73.5, 16.34, 1.2, 1.15, 0.97, 0.94, 0.9, 0.89, 0.81, 0.31
Our product in the 'long' tail of this list. I argued with them that besides spots #2 and #1 all the other following the tail are on a 'stand', since, probably, the standard deviation will be much bigger that the points that separates everyone in the tail.
So the question is: How may I calculate the standard deviation having only these percentual values available?