Statistics Lesson 1.2.notebook January 07, 2016 DATA CLASSIFICATION Data sets can consist of two types of data: Qualitative Data ­ data consisting of attributes, labels, or nonnumerical entries. Quantitative Data ­ data consisting of numerical measurements or counts. Suggested retail prices of several Honda vehicles. Model Suggested retail price Accord Sedan $21,680 Civic Hybrid $24,200 Civic Sedan $18,165 Crosstour $27,230 CR­V $22,795 Fit $15,425 Odyssey $28,675 Pilot $29,520 Ridgeline $29,450 a. Identify the two data sets. b. Decide whether each data set consists of numerical or nonnumerical entries. c. Specify the qualitative data and the quantitative data. 1 Statistics Lesson 1.2.notebook January 07, 2016 Another characteristic of data is its level of measurement. The level of measurement determines which statistical calculations are meaningful. The four levels of measurement, in order from lowest to highest, are nominal, ordinal, interval, and ratio. Nominal Level of Measurement ­ qualitative only. Data at this level are categorized using names, labels, or qualities. No mathematical computation are mad at this level. Ordinal Level of Measurement ­ Data is qualitative or quantitative. Data at this level can be arranged in order, or ranked, but differences between entries are not meaningful. EXAMPLE 2: Page 10 The two data sets shown are the top 5 grossing movies of 2012 and movie genres. The first data set lists the ranks of five movies. The set consists of ranks1, 2, 3, 4, and 5. These can be ranked in order so this data is at the ordinal level. The ranks have no mathematical meaning. The second set only lists genres of movies. No mathematical computations can be made and the names cannot be ranked, so these data are at the nominal level. Determine whether the given data are at the nominal or ordinal level. 1. The final standings for the Pacific Division of the NBA. 2. A collection of phone numbers. a. Identify what each data set represents. b. Specify the level of measurement and explain why. 2 Statistics Lesson 1.2.notebook January 07, 2016 The two highest levels of measurement consist of quantitative data only, interval level of measurement and ratio level of measurement. Interval Level of Measurement ­ data that can be ordered, and meaningful differences between data entries can be calculated. At the interval level, a zero entry simply represents a position on the scale; the entry is not an inherent zero. Ratio Level of Measurement ­ similar to data at the interval level, with the added property that a zero entry is an inherent zero. A ratio of two data entries can be formed so that one data entry can be expressed as a multiple of another An inherent zero is a zero that implies "none." For instance, the amount of money you have in a savings account could be zero dollars. In this case zero represents no money, so it is an inherent zero. On the other hand, a temperature of 0o F does not represent a condition where no heat is present. The "0" is just a position on the Fahrenheit scale. It is not an inherent zero. EXAMPLE 3: Page 11 Both sets of data contain quantitative data. It makes sense to find the difference between specific dates. But it does not make sense to say one year is a multiple of another. So the New York Yankees' world series victories would be at the interval level. Using the home run totals, it makes sense to say that Baltimore hit 39 more home runs than Tampa Bay did and New York it 1.5 times as many home runs as Detroit. So this data is at the ratio level. 3 Statistics Lesson 1.2.notebook January 07, 2016 Try it yourself: Determine whether the data are at the interval level or at the ratio level. 1. The body temperatures (in degrees Fahrenheit) of an athlete during an exercise session 2. The heart rates (in beats per minute) of an athlete during an exercise session. a. Identify what each set represents. b. Specify the level of measurement and explain why. Subtract Determine whether Level of Put data in Arrange data data on data value is a measurement categories in order values multiple of another Nominal Yes No No No Ordinal Yes Yes No No Interval Yes Yes Yes No Ratio Yes Yes Yes Yes 4 Statistics Lesson 1.2.notebook January 07, 2016 Summary of the four levels of Measurement Example of a data set Meaningful calculations Types of shows televised by a network Put in a category. Nominal Level Comedy Documentaries (Qualitative data) For instance, a show could be put Drama Cooking into one of the categories shown. Reality Shows Soap Operas Motion Picture of America Ratings Ordinal Level G General Audience Put in a category and in order. (Qualitative or PG Parental Guidance Suggested For instance, a PG rating has a quantitaive data) PG ­ 13 Parents Strongly Cautioned stronger restriction than a G R Restricted rating. NC ­ 17 No one 17 and under admitted Interval Level Average monthly Temps for Denver, CO Put in a category, in order and find (Quantitative data) Jan 30.7 Jul 74.2 differences between values. Feb 32.5 Aug 72.5 For instance, 72.5 ­ 63.4 = 9.1. Mar 40.4 Sep 63.4 August is 9.1 degrees warmer than Apr 47.4 Oct 50.9 September. May 57.1 Nov 38.3 Jun 67.4 Dec 30.0 Average monthly precip for Orlando, FL Ratio Level in inches. Put in a category, in order, find (Quantitative Level) Jan 2.35 Jul 7.27 differences between values, and Feb 2.38 Aug 7.13 find ratio of values. Mar 3.77 Sep 6.06 for instance, 7.58÷3.77≈2. So, Apr 2.86 Oct 3.31 there is about twice as much May 3.45 Nov 2.17 precipitation in June as in March. Jun 7.58 Dec 2.58 5 Statistics Lesson 1.2.notebook January 07, 2016 P. 13 7 ­ 31 odds 6.