1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 1.2 Data Classification

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. QualitativeQuantitative Descriptions and labels Counts and measurements Qualitative vs. Quantitative: Introduction to Statistics 1.2 Data Classifications HAWKES LEARNING SYSTEMS math courseware specialists

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1.4: Classifying Data as Qualitative or Quantitative a.Shades of red paint in a home improvement store { qualitative, quantitative } b.Rankings of the most popular paint colors for the season { qualitative, quantitative } c.Amount of red primary dye necessary to make one gallon of each shade of red paint { qualitative, quantitative } d.Numbers of paint choices available at several stores { qualitative, quantitative }

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. QualitativeQuantitative Continuous Usually measurements Continuous vs. Discrete: Introduction to Statistics 1.2 Data Classifications HAWKES LEARNING SYSTEMS math courseware specialists Discrete Usually counts of things Note: once you’ve picked “Qualitative”, there is no such thing as “Discrete or Continuous?” Those are subclassifications of Quantitative only.

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1.5: Classifying Data as Continuous or Discrete a.Temperatures in Fahrenheit of cities in South Carolina: quantitative and { discrete, continuous } b.Numbers of houses in various neighborhoods in a city: quantitative and { discrete, continuous } c.Numbers of elliptical machines in every YMCA in your state: quantitative and { discrete, continuous } d.Heights of doors quantitative and { discrete, continuous }

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Levels of Measurement Nominal Names Ordinal Order Interval 0 is a placeholder Ratio 0 means the absence of something Introduction to Statistics 1.2 Data Classifications HAWKES LEARNING SYSTEMS math courseware specialists

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Levels of Measurement Nominal Names Introduction to Statistics 1.2 Data Classifications HAWKES LEARNING SYSTEMS math courseware specialists NOMINAL – Names, Categories Calculations are not applicable. Example: Favorite Pizza Topping

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Levels of Measurement Nominal Names Ordinal Order Introduction to Statistics 1.2 Data Classifications HAWKES LEARNING SYSTEMS math courseware specialists ORDINAL – Can be arranged in a meaningful order But arithmetic calculations are not applicable. EXAMPLE – The seat number on your admission ticket to an event.

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1.7: Classifying Data as Nominal or Ordinal Determine whether the data are nominal or ordinal. a.The seat numbers on your concert tickets, such as A23 and A24 Qualitative and { Nominal, Ordinal } b.The genres of the music performed at the 2013 Grammys Qualitative and { Nominal, Ordinal }

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Levels of Measurement Nominal Names Ordinal Order Interval 0 is a placeholder Introduction to Statistics 1.2 Data Classifications HAWKES LEARNING SYSTEMS math courseware specialists INTERVAL – 0 might be present but it doesn’t mean the absence of something. Addition & Subtraction okay. Multiplication & Division not applicable EXAMPLES: Fahrenheit temps, Celsius, too, Certain exam scores (like IQ test), Calendar dates

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Levels of Measurement Nominal Names Ordinal Order Interval 0 is a placeholder Ratio 0 means the absence of something Introduction to Statistics 1.2 Data Classifications HAWKES LEARNING SYSTEMS math courseware specialists RATIO – Zero really means the absence of something Multiplication and Division make sense. EXAMPLES: Kelvin temperature, Price of a product, Time to run a race

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1.8: Classifying Data by the Level of Measurement The birth years of your classmates are collected. What level of measurement are these data? Nominal or Ordinal or Interval or Ratio? ___________ Solution Birth years can be ordered. It is also meaningful to subtract years to determine the difference in age. However, the year 0 A.D. does not mean the beginning of time. Therefore, birth years are at the interval level of measurement.

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1.9: Classifying Data by the Level of Measurement Consider the ages in whole years of US presidents when they were inaugurated. What level of measurement are these data? Nominal or Ordinal or Interval or Ratio? ___________ Solution The ages of US presidents are measurable, can be ordered, and an age of zero indicates the absence of life. Therefore, ages are at the ratio level of measurement. In contrast to Example 1.8, involving birth years, you can be twice as old as someone else.

14. Classify the Credit Score measurement Qualitative or Quantitative? ________________ Nominal or Ordinal or Interval or Ratio? ___________ (illustration from some web site, maybe my bank?)

15. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1.10: Classifying Data a.Finishing times for runners in the Labor Day 10K race Qualitative or Quantitative? _______________ Discrete or Continuous or Neither? ___________ Nominal or Ordinal or Interval or Ratio? ___________ b.Colors contained in a box of crayons Qualitative or Quantitative? _______________ Discrete or Continuous or Neither? ___________ Nominal or Ordinal or Interval or Ratio? ___________

16. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1.10: Classifying Data c.Boiling points (on the Celsius scale) for various caramel candies Qualitative or Quantitative? _______________ Discrete or Continuous or Neither? ___________ Nominal or Ordinal or Interval or Ratio? ___________ d.The top ten Spring Break destinations Qualitative or Quantitative? _______________ Discrete or Continuous or Neither? ___________ Nominal or Ordinal or Interval or Ratio? ___________

17. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1.4: Classifying Data as Qualitative or Quantitative (cont.) Solution a.Shades of paint are descriptions and cannot be measured, so these are qualitative data. b.Rankings are numeric but not measurements or counts, so these are qualitative data. c.The amounts of dye needed are measured and therefore are quantitative data. d.The numbers of paint choices must be counted, so they are quantitative data as well.

18. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1.5: Classifying Data as Continuous or Discrete (cont.) a.Temperatures could be measured to any level of precision based on the thermometer used, so these are continuous data. b. Numbers of houses are discrete data because houses are counted in whole numbers. A house under construction is still a house. c. The numbers of elliptical machines are counts, so these are discrete data. d. Heights are measurements and again, depending on the ruler, the heights could be measured to any level of precision, so they are continuous data.

19. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1.7: Classifying Data as Nominal or Ordinal (copy) Solution a.Seat numbers are ordinal because there is a meaningful order to the data, namely, the position in the theater. b.Despite the fact that you may have your own personal preference for specific genres of music, there is no standard order. Therefore, music genres are nominal data.

20. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1.10: Classifying Data (cont.) Solution a.The amount of time it takes for each runner to run the race is quantitative since calculations performed on these data are meaningful. A finishing time is a measurement, therefore the data are continuous. Differences between finishing times are meaningful, and a time of zero represents the absence of racing. We could also say that Andrew finished the race in half of Peyton’s time; thus, the data are at the ratio level of measurement.

21. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1.10: Classifying Data (cont.) b.Colors are labels, so these data are qualitative. Qualitative data are neither discrete nor continuous. There are many ways to order colors, such as alphabetically or based on the color spectrum. However, when discussing colors of crayons, order is not the primary factor, as opposed to data such as rankings, in which order is important. Therefore, the data are at the nominal level of measurement.

22. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1.10: Classifying Data (cont.) c.Calculations can be performed on boiling points because they are measurements, making these data quantitative. Temperatures are measurements, so the data are continuous. For the Celsius scale, a temperature of zero degrees is simply a placeholder and does not indicate the absence of heat. Therefore, data from the Celsius scale are always at the interval level of measurement.

23. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1.10: Classifying Data (cont.) d.Since the rankings cannot be meaningfully added or subtracted, the data must be qualitative. Qualitative data are neither discrete nor continuous. The rankings are in a specific order, so the data are at the ordinal level of measurement.