The "rectangles" were just for illustration. Other than that, they are just numbers -- in this case, real data for the process I am analyzing.

Got it.

Using my suggested analysis on your data, I get 70.2% within 1 SD of the mean, 96.7% within 2SD and just 2 of the 57 at 2SD or above.

I tried it with over 1,100 random data points and got 67.4% within ±1SD , 96.1% within ±2SD, and 3.9% over 2SD. These compare well to the theoretical 68, 95 and 5% values for a perfect bell curve.

My analysis is visualized pretty well in the chart above, if x an y were independent. The key difference is that I normalize the distributions (subtract the mean from each point and divide by the SD) to produce a circle instead of an ellipse. That way, the distance from the central mean is a constant radius.

 

Got it.

Using my suggested analysis on your data, I get 70.2% within 1 SD of the mean, 96.7% within 2SD and just 2 of the 57 at 2SD or above.

I tried it with over 1,100 random data points and got 67.4% within ±1SD , 96.1% within ±2SD, and 3.9% over 2SD. These compare well to the theoretical 68, 95 and 5% values for a perfect bell curve.

My analysis is visualized pretty well in the chart above, if x an y were independent. The key difference is that I normalize the distributions (subtract the mean from each point and divide by the SD) to produce a circle instead of an ellipse. That way, the distance from the central mean is a constant radius.

The suggested analysis from post #6? Yes, I think it makes sense now.

I'm not following how you choose the radius. What is the radius for 1 SD?

 

My analysis:
1. Compute normalized X and Y for each datum: normalized x = (X - Xmean)/(SDx)
This transforms your X and Y data to a mean of zero and a SD of 1
2. Calculate the distance of each normalized x,y pair from the origin (the average dimensions). R = sqrt(x^2 + y^2)
3. If you want to compare the distribution of these results to a normal distribution, you can normalize the R values to again give mean zero and SD=1. This also allows you to pick the points within a specific range of SDs away from the mean.