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Mastering Data Analysis and Graphing Techniques

Learn how to interpret and present complex data effectively through various graphs. Enhance your skills in data analysis, interpolation, and graphing for insightful data visualization. Dive into multi-dimensional imaging and advanced graphing methodologies.

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Mastering Data Analysis and Graphing Techniques

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  1. Data Analysis & Graphing

  2. Suppose I gave you a table of data

  3. A long, long table… How does one make sense of all this data?

  4. Surface temperature (last Sunday) y x The figure is capable of revealingpatternsthat are not obvious in the data!

  5. Dependence on Time (last Sunday) noon 4:00 pm 9:00 am 5:00 am

  6. It’s evident that… Figures can • Re-tell the data • Reveal patterns • tell a story

  7. Multi-dimensional imaging Consider an enormous data table containing frequencies and the variables x, y, t,andT.

  8. Wind velocity… what’smissing?

  9. Velocity is a vector

  10. Many types of graphs

  11. Data summing to 100%...

  12. Where do WIE students live?

  13. Where do commuter students live (2006)? Residential Commuter

  14. Graphing requirements • Axis labels • Unit designations • Title • Legend • Caption • A story

  15. Scaling – telling a BAD story

  16. 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?

  17. When is a table better than a figure? Five significant digits

  18. What’s the density of a 7% mixture? The table shows that the density is 0.98347 g/cm3

  19. Data Analysis: Linear Interpolation What is the density of a 5.5% ethyl alcohol solution at 25 C? Determine by linear interpolation!

  20. Data Analysis: Linear Interpolation To solve, assume a linear relationship between: • Density and temperature and/or • Density and % ethyl alcohol

  21. 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.

  22. Data Analysis: Bilinear Interpolation To solve, assume a linear relationship between: • Density and temperature and • Density and % ethyl alcohol 5.5%, T=23C *

  23. Practice Problem… then break

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