[golike]

We actually started with a linear scale, but ended up switching to a log scale. Scaling linearly says, "how much more expensive are the high end homes than the low end (subtraction)?" With the log scale we're saying, "how many more times expensive is the high end than the low end (multiplication)?"

Scaling linearly allows big values to skew the results. Imagine a neighborhood where the high end is $20m and the low end $10m, giving us an absolute difference of $10m. Another neighborhood has a $1m high end and a $500K low end, for an absolute difference of $500K. Scaled linearly, the $10m range in the first neighborhood would appear to be much much bigger than the $500K range of the second.

But if we use a log scale, instead of asking what the absolute difference is, we're asking relatively how much more expensive is the high than the low end. Using our two example neighborhoods, both would result in a 2x difference, and thus both would have the same range of prices.

It's easy to point out where all the most expensive homes are, and scaling linearly does just that. But looking at the relative differences in prices provides a much more useful way of comparing different neighborhoods (or even cities if we look nationwide), because it accounts for the natural variances in prices in different areas.

[tgrass]

Thank you very much for the thorough reply.

I don't suppose you have an image of the linear version?

[golike]

Sure do. http://cl.ly/3L223H1f2v1u3t0I3C2s

[tgrass]

Many thanks.

I prefer the linear story (not for the range-index though): it shows how consistently extreme the high end is from the median relative to the distance the low end is from the median (from a dense concentration of homes just above the median?).