The following table lists the common scenarios where weighted average/alligation is applicable. And what needs to be used as weights in the scenario. Disclaimer: This is just a cheat sheet and is not the ideal way to learn; the perfect logical way, so that you can figure out what is the weight yourself, is explained in the concept videos in the course.
| If $A_1$, $A_2$, …. are: | Then $w_1$, $w_2$, …. are: |
|---|---|
| 1. Average of a group. Could be any average measure e.g. average age or height or weight of boys; average amount each has. | Number of observations in the group |
| 2. Rate of a lot (purchase or sale) e.g. Rs/kg or Rs/lt or Rs/number. | The Quantity of the lot i.e. kg or lts or numbers. |
| 3. Percentage obtained in a subject or group | Maximum marks of the subject or group |
| 4. Profit Percentage | Cost |
| 4.1 Profit Percentage on an article | CP of the article |
| 4.2 Profit Percentage on a lot | Total Cost of the lot i.e. Rate × Quantity Sub-case: If the different lots have the same Rate, then the ratio of weights is same as ratio of Quantity (Nos or Kgs or Lts) and thus just Quantity will also suffice as the weight to be used in finding weighted average. Similarly if the lots have the same quantity, then just the Rate can be used as weight. |
| 5. Interest Rate on a deposit/loan | Principal Amount of deposit/loan |
| 6. Speed (kmph or m/s) for a part | Time duration of the part |
| 7. Milk Percentage or Proportion in a mixture/solution | Volume (total, and not just milk) of the mixture/solution |
| 8. Density i.e. weight per volume e.g. kg/litres CAT has a question on this, but the unit was not given directly, see my comment to this post. | Volume |
| 9. Used in DI Growth Rate in Sales of different category/regions. | Sales amount of the different category/region |
| 10. Used in DI Market Share of a brand/company in different category/regions. | The Market Size of the different category/regions |
| 11. Pace for a part Pace is reciprocal of speed i.e. time taken per unit distance e.g. min/km | Distance of the part |
| 12. Run-rate, specifically runs/over, for a part | Number of overs in the part |
| 13. Batting Average, specifically runs/matches, for a series | Number of matches in the series |
| 14. Bowling Average, specifically (runs conceded)/(wickets taken), for a series | Number of wickets taken in the series |
If I have missed any common scenario or you have used weighted average in an unusual setting, please suggest it in the comments and I will include it in this list. Thanks.
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