Graphs & Data

Describing Data The distribution of a variable tells us what values the variable takes, how often it takes those values, and shows the pattern of variation Categorical Categorical –Bar graph –Segmented Bar Graph –Pie chart Quantitative Quantitative –Line graph –Dotplot –Stemplot (Stem & leaf) –Histogram (Frequency distribution) –Boxplot

What type of graph would display the following data?

Bar, Segmented Bar, & Pie Charts

Line Graphs: showing change over time Time on the horizontal axis Time on the horizontal axis Connect points to show change over time Connect points to show change over time Look for an overall pattern or trend (increasing, decreasing, or steady) Look for an overall pattern or trend (increasing, decreasing, or steady) Look for striking deviations (big dips or spikes) Look for striking deviations (big dips or spikes) Look for seasonal variation –repetitions that occur every year Look for seasonal variation –repetitions that occur every year Price of Gasoline

Misleading Graphs Beware of scaling Beware of scaling

Misleading Graphs

CNN’s fixed graph

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? 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 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

Which graph is better?

What are some problems with this graph?

What’s wrong here?

Ways that Graphs may be Manipulated Scale and Axis Manipulation (Line, Bar Graphs) Scale and Axis Manipulation (Line, Bar Graphs) Cropping to focus on desirable information (Especially w/ Line Graphs) Cropping to focus on desirable information (Especially w/ Line Graphs) Three dimensional effects (e.g., perspective & “volume”) Three dimensional effects (e.g., perspective & “volume”) Pictorial Embellishments (e.g., “cartoon” effects, leading the readers’ eye) Pictorial Embellishments (e.g., “cartoon” effects, leading the readers’ eye) Mathematical Errors Mathematical Errors

What do all Graphs need? Title Title Labels Labels Legend Legend Accurate scaling Accurate scaling Simplicity so the data is easy to read Simplicity so the data is easy to read