# Ratio scale

The ratio scale , also known as the rational scale , ratio scale or proportional scale , is the highest level in statistics . It is a metric scale, but unlike the interval scale, there is an absolute zero point (e.g. blood pressure, temperature in Kelvin, age). Only at this scale level are multiplication and division meaningful and permitted. Relationships between characteristic values ​​can therefore be created (e.g. for a number and characteristic values ). ${\ displaystyle x = \ alpha y}$${\ displaystyle \ alpha}$${\ displaystyle x, y}$

## description

Characteristic values ​​are entered on a ratio / rational scale for which the following applies:

• Characteristic values ​​are shown as numbers
• for the numerical values ​​there is a natural zero point and
• the unit of measurement is defined arbitrarily (see absolute scale )

In the case of ratio scales, the numbers correspond to the strength of the characteristic values. Permissible statements are e.g. B. "Mr. X has grown by 15%".

## Examples

The table below contains examples of ratio-scaled features for temperature, time, weight, price, speed and length measurements.

feature Zero point
Temperature in Kelvin Absolute zero
Duration no duration
Dimensions no mass
price free
speed no speed, standstill
distance no distance

## Possible operations

The following operations can be performed with features that measure on a ratio scale:

• Compare on identity
• Size comparisons
Multiplicative transformations of the type with are permitted . ${\ displaystyle y = \ alpha x}$${\ displaystyle \ alpha> 0}$