# Linear vs Logarithmic Graphs

Annotation category:
Chapter 3

 Note:

As you will see below, for one of our graphing examples we collected data from the faculty teaching in this year's Frontiers of Science course. Two of the items sampled were age and distance to the faculty member's childhood home. The ages spanned the expected range of 25 to 65, but the distances ranged over a much larger set of values -- from down the street to the other side of the world. Plotting these points on a linear plot leads to an uninformative graph, with most of the points crammed against the lower axis:
IMAGE 1 BELOW:
Age of this course's faculty vs. the distance from Columbia at which they grew up. Note how on this linear scale more than half the points are so close to the y=0 line than it is difficult to see distinctions.

If instead we plot the logarithm of the distance on the y-axis, we can easily see the full range of points spread out.
IMAGE 2 BELOW:
The same data as above, plotted now as the logarithm (base 10: 1 = 10^1 = 10km, 2 = 10^2 = 100 km, etc.) of the distance vs. age on a linear scale. The points are now distributed so the full information is easily accessible.

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