Calculate price based on score using distribution

Question

Hopefully I can make sense of this. I'm writing a program that requires pricing of items. For an example let's say houses. Items are evaluated and given a score. Given that these scores are normally distributed, but prices have a right-skewed distribution I would like to be able to calculate the asking price of each item. It's been a long time since I've done this kind of math, and I'm trying to remember how to do it. I have some current statistics including total number of items, mean, mode, range and median of current item prices.

 

For example, let's say there is a mean of about 300,000, a median of about 240,000, a mode of 250,000, and a range between 67,000 - 800,000, and 320 houses total. If I have  the item's score, can I calculate it's likely price? Any help you can give is appreciated.

Answer 1

Are the standard deviations between score and price the same?

 

You will need them to convert them to z-scores.

------------------------------------------------------------------------------------------

Well then we may be better off using least squares regression
and find the slope and intercept of the best fit trend line.
All you have to do is come up with some data in the form of
ordered pairs (score, price). We can then find the slope
and intercept for the best fit trend line. There's nothing easier
than a linear function!!!

For example, since we got normal distribution with compatible
variances, let us suppose that the scores range from zer0 to 100.

Then the slope CAN be:
(800000-67000)/(100 - 0) = 7330

The equation of the line is then price = 7330 * score + 67000.
Notice that a house that scores zer0 prices at 67000 and
a house that scores 100 prices at 800000.

A house that scores 50 prices at 7330*50+6700 = 433500.