12 CHAPTER 1 Introduction to Statistics The tables below summarize which operations are meaningful at each of the four levels of measurement. When identifying a data set’s level of measurement, use the highest level that applies. Level of measurement Put data in categories Arrange data in order Subtract data entries Determine whether one data entry is a multiple of another Nominal Yes No No No Ordinal Yes Yes No No Interval Yes Yes Yes No Ratio Yes Yes Yes Yes Summary of Four Levels of Measurement Example of a data set Meaningful calculations Nominal level (Qualitative data) Types of Shows Televised by a Network Comedy Documentaries Drama Cooking Reality Shows Soap Operas Sports Talk Shows Put in a category. For instance, a show televised by the network could be put into one of the eight categories shown. Ordinal level (Qualitative or quantitative data) Motion Picture Association of America Ratings Description G General Audiences PG Parental Guidance Suggested PG-13 Parents Strongly Cautioned R Restricted NC-17 No One 17 and Under Admitted Put in a category and put in order. For instance, a PG rating has a stronger restriction than a G rating. Interval level (Quantitative data) Average Monthly Temperatures (in degrees Fahrenheit) for Denver, CO Jan 30.9 Jul 73.6 Feb 32.8 Aug 71.5 Mar 40.0 Sep 62.4 Apr 47.5 Oct 50.3 May 57.2 Nov 38.6 Jun 67.0 Dec 30.0 (Source: National Oceanic and Atmospheric Administration) Put in a category, put in order, and find differences between data entries. For instance, 71.5 - 62.4 = 9.1°F. So, August is 9.1°F warmer than September. Ratio level (Quantitative data) Average Monthly Precipitation (in inches) for Orlando, FL Jan 2.35 Jul 7.27 Feb 2.38 Aug 7.13 Mar 3.77 Sep 6.06 Apr 2.68 Oct 3.31 May 3.45 Nov 2.17 Jun 7.58 Dec 2.58 (Source: National Oceanic and Atmospheric Administration) Put in a category, put in order, find differences between data entries, and find ratios of data entries. For instance, 7.58 3.77 ≈ 2. So, there is about twice as much precipitation in June as in March.
RkJQdWJsaXNoZXIy NjM5ODQ=