Graphing

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When collecting data—whether establishing relationships between two variables or identifying correlations across multiple samples—we use graphs to visualize those connections.

However, it is essential to understand the type of data you are collecting and how to represent it effectively. Using the correct graph allows you to accurately determine the mathematical relationships within your data sets.


Choosing the Right Graph

First, we need to determine the appropriate graph type based on the variable you are analyzing: nominal vs. ordinal or discrete vs. continuous (and thus bar graphs vs. line graphs vs. histograms).

This video examines the different types of variables you encounter during data collection and explains why specific graph types are best suited to represent them.

Linearizing Data

When we graph variables that share a relationship, the graph allows us to determine their exact mathematical model.

For example, if we graph y vs. x and the result is linear, the slope represents the constant of proportionality (y = mx). If we then extrapolate the line to the y-axis, we can also determine the y-intercept (c), giving y = mx + c.

If the plot of y vs. x forms a curve (such as a parabola), plotting y vs. x2 instead will yield a straight line. The slope of this new line gives us the coefficient of proportionality (y = mx2).

Many relationships in physics follow standard mathematical forms:

  • Linear: y = mx
  • Square: y = mx2
  • Inverse: y = m/x  (or y = mx-1)
  • Inverse Square: y = m/x2  (or y = mx-2)
However, physics relationships are not limited to cases where the power of y is 1. Variables can also involve fractional powers (such as square roots), exponential relationships, and logarithms.

Linearizing data is about determining the relationship between variables, specifically, the independent and dependent variables. In this video I show you how to turn non linear graphs to linear graphs and thus determine the mathematical equation that describes the variable.

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