A long, long table… How does one make sense of all this data?
Surface temperature (last Sunday) y x The figure is capable of revealingpatternsthat are not obvious in the data!
Dependence on Time (last Sunday) noon 4:00 pm 9:00 am 5:00 am
It’s evident that… Figures can • Re-tell the data • Reveal patterns • tell a story
Multi-dimensional imaging Consider an enormous data table containing frequencies and the variables x, y, t,andT.
Where do commuter students live (2006)? Residential Commuter
Graphing requirements • Axis labels • Unit designations • Title • Legend • Caption • A story
Graphs in Labs • How did you present your data in the college rankings lab? • How did you present your data in the materials lab? • Why?
When is a table better than a figure? Five significant digits
What’s the density of a 7% mixture? The table shows that the density is 0.98347 g/cm3
Data Analysis: Linear Interpolation What is the density of a 5.5% ethyl alcohol solution at 25 C? Determine by linear interpolation!
Data Analysis: Linear Interpolation To solve, assume a linear relationship between: • Density and temperature and/or • Density and % ethyl alcohol
Data Analysis: Bilinear Interpolation What if there is a non-linear relationship between x and y? y x Over small Δx, can still approximate a linear relationship between x and y.
Data Analysis: Bilinear Interpolation To solve, assume a linear relationship between: • Density and temperature and • Density and % ethyl alcohol 5.5%, T=23C *