Scale Distortion Math Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
mediumA graph uses a logarithmic scale for a dataset ranging from 1 to 1,000,000. Explain when a log scale is appropriate vs. misleading, and how to label it correctly.
Solution
- 1 Log scale appropriate when: data spans multiple orders of magnitude (1 to 1,000,000 = 6 orders); showing multiplicative (exponential) growth; relative changes are more meaningful than absolute ones
- 2 Log scale label: each gridline represents 10× increase (1, 10, 100, 1000, 10000, 100000, 1000000); must be explicitly labeled as 'log scale'
- 3 Misleading if: used without disclosure, applied to data that doesn't span orders of magnitude, or compared with linear-scale charts without noting the difference
- 4 Correct labeling: 'y-axis: log scale (base 10)' or label each gridline with actual values
Answer
Log scales are appropriate for multi-order-magnitude data but must be clearly labeled; unlabeled log scales are misleading.
Logarithmic scales are powerful tools for wide-ranging data but require clear disclosure. Exponential growth looks linear on a log scale (appropriate); linear growth looks curved (potentially misleading). Always label axis type explicitly.
About Scale Distortion
Scale distortion occurs when a graph's axis does not start at zero or uses inconsistent intervals, making small differences appear large or large differences appear small.
Learn more about Scale Distortion →More Scale Distortion Examples
Example 1 easy
Two graphs show the same data (unemployment: 4% to 5%). Graph A: y-axis from 0–10%. Graph B: y-axis
Example 3 easyA pictograph shows a 2021 salary twice as large as a 2020 salary by doubling both the height AND wid
Example 4 hardA company's revenue chart has an x-axis with uneven time intervals (2010, 2012, 2016, 2017, 2018). T