Question

What is the statistical significance of one standard deviation? two standard deviations?

Answer 1

When we do an estimate, we come up with two major values: the expected value and the standard deviation. The EV is a bit like the average value. We throw a pair of dice some N trials and get an average score by SUM(x)/N = average = EV. x is the score (the point) for each trial (toss).

Which means in practical terms, the probability is highest that we'll throw EV on the next toss. For fair die (no cheating) EV = 7...lucky seven. But those scores x don't all fall on the 7. There will be some 2, 3, 4, 5, 6...8, 9 , 10, 11, and 12s as well as those 7's. And how those other scores spread out in their distribution around that lucky 7 is measured by the SD.

There is a rough guesstimate for SD's of a special probability density curve caller the normal or bell curve. It looks like this. SD = (max - min)/6 or (max - min)/4, there's a difference of opinion. [See source.] So for those fair dice, max = 12 and min = 2 are the bounding values, so SD = (12 - 2)/6 = 1.67.

The 6 says there are 6 SD that span the interval between the max and the min values. And for a bell curve, 6 SD equates to a 99% plus probability. If the 4 version is used, 4 SD equates to a 95% probability that the score (point) will lie between the max and min. I like the 6 SD version for dice as 99% is all but 100% and we know fair dice have to come up with something between 2 and 12, there are no other values they can come up with. These are rough and should not be used in critical design work.

So, for the dice we now have X = EV +/- nSD where X is the randomly derived score (the point). n is the number of SD's assumed. And to answer your question, for the bell curve:

+/- 1 SD ~ about 67% probability of finding the value X in that interval around the EV
+/- 2 SD ~ about 95% probability
+/- 3 SD ~ about 99% probability