Editing Level of measurement (section)

===Interval scale===
The interval type allows for defining the ''degree of difference'' between measurements, but not the ratio between measurements. Examples include ''[[temperature scale]]s'' with the [[degree Celsius|Celsius scale]], which has two defined points (the freezing and boiling point of water at specific conditions) and then separated into 100 intervals, ''date'' when measured from an arbitrary epoch (such as AD), ''location'' in Cartesian coordinates, and ''direction'' measured in degrees from true or magnetic north. Ratios are not meaningful since 20&nbsp;°C cannot be said to be "twice as hot" as 10&nbsp;°C (unlike temperature in [[kelvin]]s), nor can multiplication/division be carried out between any two dates directly. However, ''ratios of differences'' can be expressed; for example, one difference can be twice another; for example, the ten-degree difference between 15&nbsp;°C and 25&nbsp;°C is twice the five-degree difference between 17&nbsp;°C and 22&nbsp;°C. Interval type variables are sometimes also called "scaled variables", but the formal mathematical term is an [[affine space]] (in this case an [[affine line]]).

====Central tendency and statistical dispersion====
The [[mode (statistics)|mode]], [[median]], and [[arithmetic mean]] are allowed to measure central tendency of interval variables, while measures of statistical dispersion include [[range (statistics)|range]] and [[standard deviation]]. Since one can only divide by ''differences'', one cannot define measures that require some ratios, such as <!--- the studentized range or. --- Error: studentized range is a ratio of a difference (range) to a root-mean-square difference (standard DEVIATION from the mean ---> the [[coefficient of variation]]. More subtly, while one can define [[Moment (mathematics)|moments]] about the [[Origin (mathematics)|origin]], only central moments are meaningful, since the choice of origin is arbitrary. One can define [[standardized moment]]s, since ratios of differences are meaningful, but one cannot define the coefficient of variation, since the mean is a moment about the origin, unlike the standard deviation, which is (the square root of) a central moment.