How Quantities Combine: Understanding Data
Weights for importance
Use weights to show that some marks or ratings count for more.
Weights need not be amounts; they can show importance.
Rehmat scored 60% in internals, 64% in the project and 73% in the final exam, combined in the ratio 3 : 2 : 5. Annual score = (60 × 3 + 64 × 2 + 73 × 5)/(3 + 2 + 5) = 673/10 = 67.3%.
Think of it as a list. It is as if each score were written down that many times: 60, 60, 60, 64, 64, 73, 73, 73, 73, 73, then averaged in the ordinary way.
Same scale first. Marks out of different totals must first become fractions or percentages of their own totals: 35/50 = 70%, 44/60 ≈ 73.3%, 80/100 = 80%. Only then weight them.
Ratings work the same way: food 5, service 3, ambience 4, weighted 4 : 3 : 2, gives (20 + 9 + 8)/9 ≈ 4.11.
Use a weighted mean whenever each part should count by how much it contributes: by amount, by time, or by importance.
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