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Graphs & Data. Data--Types of Variables. Categorical or Quantitative?. Heights of people Level of education Favorite brand of food Distance traveled Zip code. Q C C Q C. Categorical Bar graph Segmented Bar Graph Pie chart. Quantitative Line graph Dotplot Stemplot (Stem & leaf)
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Categorical or Quantitative? • Heights of people • Level of education • Favorite brand of food • Distance traveled • Zip code • Q • C • C • Q • C
Categorical Bar graph Segmented Bar Graph Pie chart Quantitative Line graph Dotplot Stemplot (Stem & leaf) Histogram (Frequency distribution) Boxplot Describing DataThe distribution of a variable tells us what values the variable takes, how often it takes those values, and shows the pattern of variation
Line Graphs: showing change over time • Time on the horizontal axis • Connect points to show change over time • Look for an overall pattern or trend (increasing, decreasing, or steady) • Look for striking deviations (big dips or spikes) • Look for seasonal variation –repetitions that occur every year Price of Gasoline
Misleading Graphs • Beware of scaling
Same data, but different scales How do the scales effect our impression of the data?
Choosing Scaling • Mayor Marcus is running for a second term against a challenger. Which graph should he send to the local journalist who is reporting on crime rates?
Misleading Graphs • Beware of the pictogram • Bars should have equal width • If the entire area (width and height) is changed, there appears to be a greater increase than really exists
Ways that Graphs may be Manipulated • Scale and Axis Manipulation (Line, Bar Graphs) • Cropping to focus on desirable information (Especially w/ Line Graphs) • Three dimensional effects (e.g., perspective & “volume”) • Pictorial Embellishments (e.g., “cartoon” effects, leading the readers’ eye) • Mathematical Errors
What do all Graphs need? • Title • Labels • Legend • Accurate scaling • Simplicity so the data is easy to read