On page 10 of the datasheet under "Modifying the measurement range" it states that "The ADXRS646 scale factor can be reduced to extend the measurement range to as much as ±450°/sec by adding a single 225 kΩ resistor between RATEOUT and SUMJ." What value of resistance is used to extend the measurement rate by a random value such as +-200deg/sec. Is there a formula or relationship that can be derived?

It looks like this question was missed, and the organization around this forum has undergone several changes ever since. Sorry about that.

As a rule of thumb, assume that you are operating with 6V supply, and want to limit that rail of operation for output to 5.7V for good linearity. Therefore, you must ensure that the range you select gives you a scale factor to meet this voltage range.

The scale factor is set by the parallel combination of the output resistor with the internal 180kOhm resistor. If you use external resistor R0, then scale factor = (9mV/dps)*[(R0||180)/180] = 9*[R0/(R0+180)] mV/dps