Variables, Data, Measurements

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

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

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) cm  F sec g 4 Bluman Chapter 1

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 “ ” calculator display as your final answer.

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 ≤ x < miles

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 ≤ d < – And 0.02 means ≤ d < – And 44,716 miles means 44,716 ≤ d < 44,717

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

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