| Concept | Formula | Usage Note |
| Basic Average | $$\frac{\text{Sum of observations}}{\text{Number of observations}}$$ | The standard “Arithmetic Mean” for any set of numbers. |
| Total Sum | $$\text{Average} \times \text{Number of observations}$$ | Used to find the total value when the average and count are known. |
| Average Speed | $$\frac{2xy}{x + y}$$ | Use this when a person covers equal distances at speeds $x$ and $y$. |
| Average of $n$ Natural Numbers | $$\frac{n + 1}{2}$$ | Quickly finds the average of numbers from $1$ to $n$. |
Based on the IndiaBIX Average Formulas page, here is a concise table of the essential formulas you’ll need for aptitude tests:
Core Average Formulas
| Concept | Formula | Usage Note |
| Basic Average | $$\frac{\text{Sum of observations}}{\text{Number of observations}}$$ | The standard “Arithmetic Mean” for any set of numbers. |
| Total Sum | $$\text{Average} \times \text{Number of observations}$$ | Used to find the total value when the average and count are known. |
| Average Speed | $$\frac{2xy}{x + y}$$ | Use this when a person covers equal distances at speeds $x$ and $y$. |
| Average of $n$ Natural Numbers | $$\frac{n + 1}{2}$$ | Quickly finds the average of numbers from $1$ to $n$. |
Quick Rules for Problem Solving
- Consecutive Numbers: If the numbers are in an arithmetic progression (like 2, 4, 6, 8), the average is simply the middle term (or the average of the two middle terms).
- The “New Value” Rule: If adding a new member to a group of $n$ people changes the average from $A$ to $B$, the value of the new member is:New Value = $n \times (B – A) + B$
