Levels of Measurement

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The levels of measurement are a way of categorizing a data as one of four different categories:

Ratio Data

Interval Data

Ordinal Data

Nominal Data

An example of nominal data is blood types:

  • type A+
  • type A-
  • type B+
  • type B-
  • type AB+
  • type AB-
  • type O+
  • type O-

Another example of nominal data is sex:

  • female
  • male

Another example of nominal data is family names:

  • Alves
  • Beg
  • Chen
  • Cho
  • Choi
  • da Silva
  • Dickson
  • dos Santos
  • Esfahani
  • Fernández
  • Ferreira
  • García
  • Jung
  • Kang
  • Kerr
  • Kim
  • Krempeaux
  • Li
  • Liu
  • Martin
  • Müller
  • Pahlavi
  • Park
  • Parsi
  • Pereira
  • Rodríguez
  • Safavi
  • Sasani
  • Wang
  • Yun
  • Zhang
  • etc

Another example of nominal data is hair color:

  • brown
  • black
  • blond
  • gray
  • red
  • etc

Another example of nominal data is cities:

  • Beijing
  • Bangalore
  • Bangkok
  • Bogotá
  • Buenos Aires
  • Cairo
  • Chennai
  • Chicago
  • Chongqing
  • Dallas
  • Delhi
  • Dhaka
  • Guangzhou
  • Hyderabad
  • Kinshasa
  • Kolkata
  • Isfahan
  • Istanbul
  • Jakarta
  • Karachi
  • Lagos
  • Lahore
  • Lima
  • London
  • Los Angeles
  • Moscow
  • Nagoya
  • New York City
  • Osaka
  • Manila
  • Mexico City
  • Mumbai
  • Paris
  • Rio de Janeiro
  • São Paulo
  • Seoul
  • Shanghai
  • Shenzhen
  • Tehran
  • Tianjin
  • Tokyo
  • Toronto
  • Vancouver
  • etc

Operations

One way of understanding the levels of measurement is — what type of operations are meaningful and valid for that type of data‽

Here is a table that summarizes what operations are and are notmeaningful and valid for each levels of measurement category:

nominal ordinal interval ratio
can × and ÷ ? no no no YES
can + and - ? no no YES YES
can < and > ? no YES YES YES
can = and ≠ ? YES YES YES YES