Convert a series of values in to a relative 1-10 scale - scale

Question

Let's say I have a few sets of values like this:
Height (in inches):
John 72.3
Peter 64.5
Frank 78.5
Susan 65.8
Judy 69.0
Mary 72.7
Weight (in pounds):
John 212
Peter 232
Frank 140
Susan 355
Judy 105
Mary 76
Age (in seconds since birth)
John 662256000
Peter 1292976000
Frank 977616000
Susan 1229904000
Judy 599184000
Mary 283824000
What's the best way to convert these values into a 1-10 scale relative to the other values?
I want to be able to say John is a 6/10 on height, 10/10 on height, and a 3/10 on age (made up values) for example.
One issue I'd like to be able to avoid is having extreme values on either side distort the system too much. A very heavy or tall person shouldn't distort the entire scale.

Answer 1

In R, you can use quantile to find the deciles of the data and then findInterval to find the interval in which each observation lies.
x <- rnorm(100)
findInterval( x, quantile(x, seq(0,1,length=11))) )

Answer 2

In R
heightOrder <- order(height)
will give you the rank order of each item. If there are 10 it will go from 1-10. You could scale that to 10.
heightOrder <- heightOrder / max(heightOrder) * 10
Now that goes from 0-10. Although, now that I look at your question you asked "best way". The best way to scale depends on what you want to accomplish. You need to add more to your question to really know the best way.

Answer 3

Isn't it simply:
y = (x-min)/(max-min)*9+1
Perhaps with some rounding using
sprintf '%.0f'
use strict;
use warnings;
use List::MoreUtils qw( minmax );
my %people = (
John => { height => 72.3, weight => 212, age => 662256000 },
Peter => { height => 64.5, weight => 232, age => 1292976000 },
Frank => { height => 78.5, weight => 140, age => 977616000 },
Susan => { height => 65.8, weight => 355, age => 1229904000 },
Judy => { height => 69.0, weight => 105, age => 599184000 },
Mary => { height => 72.7, weight => 76, age => 283824000 },
);
sub scale {
my ($min, $max, $x) = #_;
return ($x-$min)/($max-$min)*9+1;
}
my ($min_height, $max_height) = minmax( map $_->{height}, values %people );
my ($min_weight, $max_weight) = minmax( map $_->{weight}, values %people );
my ($min_age, $max_age ) = minmax( map $_->{age }, values %people );
for my $name (keys %people) {
my $person = $people{$name};
printf("%-6s height: %2.0f/10 weight: %2.0f/10 age: %2.0f/10\n",
"$name:",
scale($min_height, $max_height, $person->{height}),
scale($min_weight, $max_weight, $person->{weight}),
scale($min_age, $max_age, $person->{age }),
);
}
Output:
Susan: height: 2/10 weight: 10/10 age: 9/10
John: height: 6/10 weight: 5/10 age: 4/10
Mary: height: 6/10 weight: 1/10 age: 1/10
Judy: height: 4/10 weight: 2/10 age: 4/10
Peter: height: 1/10 weight: 6/10 age: 10/10
Frank: height: 10/10 weight: 3/10 age: 7/10

Answer 4

If you want your sample to be equally distributed within each of your 1, 2, ...10, then I suggest you use quantiles. In R:
> relative.scale <- function(x) {
+ percentiles <- quantile(x, probs = seq(0,0.9,0.1))
+ sapply(x, function(v)sum(percentiles <= v))
+ }
> x <- runif(100)
> s <- relative.scale(x)
> table(s)
s
1 2 3 4 5 6 7 8 9 10
10 10 10 10 10 10 10 10 10 10