An interpretation of standard deviation
Shown above is a 3D plot, visualising an interpretation of the standard deviation of three values , and .
(I will leave it to you to decide whether this is a useful interpretation!)
The values , and are plotted along each of the axes, at the purple points.
The purple vector goes from the origin to the coordinate .
The green vector goes from the origin to the coordinate (where is the mean of , and ).
(Slide the purple points in the app to get a sense for how the vectors move.)
The two vectors are joined by a black line segment. This black line segment forms the diagonal of a red cube. The standard deviation of , and equals the side length of the red cube.
Questions:
- How/why?
- Can you draw a similar interpretation in two dimensions, for the standard deviation of two values?
- How might the interpretation extend to four values?