G2 Mathematics K210 comparison is not one operation. Two quantities can be compared by absolute difference, ratio, percentage change, rate, density, per-capita amount, index or another normalised measure. Choosing the wrong comparison can produce flawless arithmetic for the wrong question.
This one-hundred-and-tenth Learner’s Guide develops comparison-measure choice. It complements Vol 0078 Dimensional Consistency and Vol 0082 Direction-of-Change Checks.
The comparison-choice test
Ask what must be held common for the comparison to be fair. If bases differ, raw differences may mislead. If units differ, convert first. If the question asks relative change, identify the reference denominator before calculating.
1. absolute difference
For absolute difference, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
2. signed change
For signed change, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
3. ratio
For ratio, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
4. fraction of original
For fraction of original, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
5. percentage share
For percentage share, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
6. percentage change
For percentage change, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
7. percentage-point change
For percentage-point change, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
8. rate
For rate, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
9. unit rate
For unit rate, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
10. density
For density, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
11. per-capita amount
For per-capita amount, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
12. index number
For index number, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
13. scale factor
For scale factor, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
14. relative error
For relative error, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
15. absolute error
For absolute error, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
16. margin
For margin, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
17. markup
For markup, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
18. profit
For profit, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
19. return
For return, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
20. utilisation
For utilisation, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
21. occupancy
For occupancy, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
22. success rate
For success rate, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
23. error rate
For error rate, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
24. response rate
For response rate, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
25. growth rate
For growth rate, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
26. decline rate
For decline rate, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
27. speed
For speed, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
28. time per distance
For time per distance, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
29. productivity
For productivity, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
30. time per task
For time per task, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
31. fuel efficiency
For fuel efficiency, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
32. fuel consumption
For fuel consumption, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
33. population density
For population density, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
34. area per person
For area per person, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
35. frequency
For frequency, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
36. relative frequency
For relative frequency, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
37. frequency density
For frequency density, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
38. mean
For mean, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
39. median
For median, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
40. range
For range, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
41. weighted mean
For weighted mean, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
42. gradient
For gradient, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
43. change per unit x
For change per unit x, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
44. probability
For probability, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
45. odds-like comparison where defined
For odds-like comparison where defined, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
46. part-to-part ratio
For part-to-part ratio, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
47. part-to-whole ratio
For part-to-whole ratio, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
48. final/original multiplier
For final/original multiplier, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
49. original/final reciprocal
For original/final reciprocal, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
50. discount amount
For discount amount, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
51. discount rate
For discount rate, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
52. tax amount
For tax amount, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
53. tax rate
For tax rate, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
54. interest amount
For interest amount, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
55. interest rate
For interest rate, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
56. simple growth factor
For simple growth factor, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
57. compound growth factor
For compound growth factor, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
58. depreciation factor
For depreciation factor, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
59. currency quote
For currency quote, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
60. reciprocal currency quote
For reciprocal currency quote, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
61. cost per item
For cost per item, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
62. items per dollar
For items per dollar, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
63. mass per item
For mass per item, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
64. items per mass
For items per mass, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
65. flow rate
For flow rate, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
66. time per volume
For time per volume, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
67. data rate
For data rate, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
68. time per data
For time per data, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
69. work rate
For work rate, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
70. time per work
For time per work, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
71. cash runway
For cash runway, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
72. burn rate
For burn rate, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
73. capacity remaining
For capacity remaining, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
74. percentage capacity remaining
For percentage capacity remaining, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
75. raw count difference
For raw count difference, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
76. normalised difference
For normalised difference, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
77. baseline comparison
For baseline comparison, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
78. control comparison
For control comparison, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
79. before-after comparison
For before-after comparison, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
80. subgroup comparison
For subgroup comparison, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
81. same denominator comparison
For same denominator comparison, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
82. different denominator comparison
For different denominator comparison, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
83. large group versus small group
For large group versus small group, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
84. same absolute change different bases
For same absolute change different bases, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
85. same percentage change different bases
For same percentage change different bases, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
86. same final value different starts
For same final value different starts, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
87. same ratio different totals
For same ratio different totals, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
88. same mean different spread
For same mean different spread, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
89. same total different rates
For same total different rates, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
90. same rate different totals
For same rate different totals, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
91. comparison measure final rule
For comparison measure final rule, write the numerator and denominator—or state explicitly that no denominator is used. Then name the comparison question this measure answers. This prevents formulas from becoming detached from meaning.
Practice with two datasets where the ranking changes depending on the measure. Explain why absolute difference, ratio and percentage can legitimately answer different questions. The goal is not to find one universally best metric; it is to choose the metric aligned with the task.
Finally, inspect the unit. Dimensionless percentages and ratios should cancel like quantities; rates and densities retain compound units. The unit is a compact audit of what comparison you actually computed.
The denominator is the comparison frame
Many comparison errors are denominator errors. Percentage change uses the original value; margin and markup use different bases; population density uses area; per-capita measures use people. Write the denominator in words before dividing.
Links
Use the Mathematics Hub, Vol 0094 Sensitivity Checks, Vol 0086 Bounding Checks, the Examination Craft hub and the PSLE Learner’s Guide.
Official-source discipline
For the current 2027 SEC G2 school-candidate framework, use the official SEAB G2 syllabus directory and linked K210 Mathematics syllabus. Comparison-measure choice is an eduKateSengkang problem-solving framework, not an additional SEAB syllabus topic.
Final rule
Before calculating a comparison, name what the number is supposed to mean. Choose difference, ratio, percentage, rate or normalised measure to match that meaning, and make the denominator visible.
