Eduqo
Quantitative Aptitude›Ch 1: Arithmetic Foundations›Average Masterclass
Ace SSC, Railway and Defence exams with smart average techniques.
Average is the sum of observations divided by the total number of observations. For consecutive numbers, the average is simply the exact middle value. Mastering deviation and replacement saves crucial seconds in exams.
Memory Hooks
| Type | Concept / Rule | Shortcut |
|---|---|---|
| First n numbers | Sum of 1 to n | (n + 1) / 2 |
| Replacement | One leaves, one joins | Old ± (Diff × n) |
| Cricket Run Rate | Target after match | Old + (Inc × Rem) |
SUM
(Total of values)
Total of values
Average multiplied by total gives total sum.
MIDPOINT
(Middle of series)
Middle of series
Average of 5 consecutive odd numbers is the 3rd number.
REPLACE
(New member swap)
New member swap
If average increases by 2 for 10 men, total increases by 20.
CRICKET
(Run rate math)
Run rate math
Add extra runs needed to previous average for target.
Confusing sum with averageAlways divide by count
Students often forget to divide the final sum by the total number of items.
Adding instead of subtractingCheck sign in replacement
When a member leaves and is lighter, average decreases. Watch out for signs.
Wrong multiplier in run rateMultiply by total innings
In cricket questions, ensure you multiply the average increment by total matches played.
Q1.The average of 5 consecutive numbers is 20. What is the largest number?
Q2.A batsman has a certain average for 11 innings. In the 12th innings, he scores 90 runs and increases his average by 5. What is his new average?