1. Variables, Data, Measurements

2. 1-2 Variables and Types of Data (Bluman 5 th Ed. – © McGraw Hill) Data Qualitative Categorical Quantitative Numerical, Can be ranked Discrete Countable 5, 29, 8000, etc. Continuous Can be decimals 2.59, 312.1, etc. 2 Bluman Chapter 1

3. More about Quantitative The box on the previous pages says it’s “Numerical” The box says it “can be ranked”

4. 1-2 Recorded Values and Boundaries (Bluman 5 th Ed. – © McGraw Hill) VariableRecorded ValueBoundaries Length15 centimeters (cm) Temperature 86  Fahrenheit (  F) Time0.43 second (sec) Mass1.6 grams (g) 14.5-15.5 cm 85.5-86.5  F 0.425-0.435 sec 1.55-1.65 g 4 Bluman Chapter 1

5. Measurements of continuous data are Inexact There is no such thing as an exact measurement. There is no infinite precision. In science, there’s an “uncertainty principle” Don’t copy “2.98372763” calculator display as your final answer.

6. Measurements are Inexact There’s an implied “betweenness” “3 miles” implies that 2.5 ≤ x < 3.5 miles Note the ≤ and the < That is on purpose! “3.0 miles” means 2.95 ≤ x < 3.05 miles “3.5” miles means 3.45 ≤ x < 3.55 miles “3.50 miles” means 3.495 ≤ x < 3.505 miles

7. An objection Odometer example: – It doesn’t change from 0.00 to 0.01 until the wheel has rotated a distance of 52.8 feet. – It doesn’t change from 0.01 to 0.02 until the wheel travels another 52.8 feet. – Therefore 0.01 means 0.010 ≤ d < 0.020 – And 0.02 means 0.020 ≤ d < 0.030 – And 44,716 miles means 44,716 ≤ d < 44,717

8. 1-2 Variables and Types of Data (Bluman 5 th Ed. – © McGraw Hill) Levels of Measurement 1.Nominal 1.Nominal – categorical (names) 2.Ordinal 2.Ordinal – nominal, plus can be ranked (order) 3.Interval 3.Interval – ordinal, plus intervals are consistent 4.Ratio 4.Ratio – interval, plus ratios are consistent, true zero 8 Bluman Chapter 1

9. 1-2 Variables and Types of Data (Bluman 5 th Ed. – © McGraw Hill) Determine the measurement level. VariableNominalOrdinalIntervalRatioLevel Hair ColorYesNoNominal Zip CodeYesNoNominal LetterGradeYes NoOrdinal ACT ScoreYes NoInterval HeightYes Ratio AgeYes Ratio Temperature(F)Yes NoInterval 9 Bluman Chapter 1