Averages and Weighted Average
Averages and Weighted Average
Average, or mean, is one of the most predictable scorers in SBI Clerk Numerical Ability, appearing both as standalone questions and as a step inside DI. The average of a set is simply the total divided by the count, but the exam rarely asks it that plainly. Instead it tests how the average shifts when a value is added or removed, or how two groups combine. Master the total-and-count view and every average question becomes a one-line calculation you can trust under time pressure.
Think in Totals, Not Averages
The single most useful habit is to convert an average into a total the moment you read it, because totals add and averages do not. If ten students average 60 marks, their total is 600; if one more student scoring 82 joins, the new total is 682 over 11, giving about 62. Working with the running total sidesteps the confusion of trying to average two averages directly. Almost every add, remove or replace question is solved cleanly by adjusting the total first and dividing only at the very end.
Average = total / count New average = (old total ± changed value) / new count
Effect of Adding or Removing a Value
When a new value equals the current average, the average is unchanged; when it is above, the average rises, and when below, it falls. A faster route uses the shortcut below: the average moves by the gap between the new value and the old average, shared over the new count. Replacement questions — a person of known weight leaves and another joins — are handled the same way by tracking only the change in total, so you never rebuild the whole sum from scratch.
Shortcut: Change in Average
For a quick answer, use: new average = old average + (added value − old average) / new count. If 5 numbers average 20 and a sixth number 32 is added, the rise is (32 − 20) / 6 = 2, so the new average is 22 without computing the total at all. The same idea handles replacement: total change divided by the count gives the shift in average directly. This one-line adjustment is the fastest method in the topic and worth drilling until it is automatic.
Weighted Average
When two groups of different sizes combine, you cannot simply average the two averages — you must weight each by its count. The weighted average is the sum of (each group's average times its size) divided by the total size. If 20 boys average 60 and 30 girls average 70, the class average is (20×60 + 30×70) / 50 = (1200 + 2100) / 50 = 3300 / 50 = 66, not the plain midpoint 65; the anchor is to use the counts as weights and always divide by the combined count.
| Situation | What happens to the average |
|---|---|
| New value = current average | No change |
| New value above average | Average rises |
| New value below average | Average falls |
| Two groups combine | Use weighted average by count |
Solved Examples
Example 1: The average of 6 numbers is 25. If a 7th number 39 is added, rise = (39 − 25) / 7 = 2, so new average = 27, no total needed.
Example 2: Class of 40 averages 50, another of 60 averages 75. Weighted average = (40×50 + 60×75) / 100 = (2000 + 4500) / 100 = 65.
✗ Averaging 50 and 75 to get 62.5 for two unequal groups | ✓ Weighting each average by its group size before dividing by 100
औसत = कुल योग / संख्या। औसत को तुरंत कुल में बदलें, क्योंकि योग जुड़ते हैं, औसत नहीं। दो असमान समूहों का भारित औसत — हर औसत को उसकी संख्या से गुणा करें।
Exam Pointer — SBI Clerk typically sets 1–2 average questions and uses the average step throughout DI, so it is very high value. Add, remove and replace types dominate. Convert to totals instantly and use the change-in-average shortcut; the classic error the paper rewards is averaging two averages of unequal groups.
60-Second Recap
- Average = total / count; turn averages into totals first.
- Add/remove/replace: adjust the total, divide at the end.
- Shortcut: rise = (new value − old average) / new count.
- Two unequal groups need a weighted average, not a plain one.