Study Guide · Chapter 14
3A. Quick Formula Reference Sheet
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Use this box as a last-minute revision sheet the night before your exam — every formula from Section 2 is listed here in compressed form for rapid recall.
| Concept | Formula |
|---|---|
| Basic average | Average = Sum of observations ÷ Number of observations |
| Sum from average | Sum = Average × Number of observations |
| Average of any AP / consecutive numbers | (First term + Last term) ÷ 2 |
| Average of first n natural numbers | (n + 1) ÷ 2 |
| Average of first n even numbers | n + 1 |
| Average of first n odd numbers | n |
| Average of squares of first n natural numbers | (n + 1)(2n + 1) ÷ 6 |
| Average of cubes of first n natural numbers | n(n + 1)² ÷ 4 |
| Weighted average (2 groups) | (n₁A₁ + n₂A₂) ÷ (n₁ + n₂) |
| Average speed, equal distances (2 speeds) | 2xy ÷ (x + y) |
| Average speed, equal distances (3 speeds) | 3xyz ÷ (xy + yz + zx) |
| Average speed, equal time | Simple average of the speeds |
| Replacement — average increases by d | New value = Old value + (n × d) |
| Replacement — average decreases by d | New value = Old value − (n × d) |
| Member joins, group average known | Joining value = New average × (n+1) − Old average × n |
| Member leaves, group average known | Leaving value = Old average × n − New average × (n−1) |
| Adding constant k to every value | New average = Old average + k |
| Multiplying every value by k | New average = Old average × k |
| Deviation (assumed mean) method | Average = Assumed mean + (Sum of deviations ÷ n) |
Keep this table bookmarked — nearly every question in Sets A and B below reduces to a direct substitution into one of these seventeen formulas.
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