Sum Calculator
A sum calculator adds a list of numbers, providing the total, count, average, minimum, and maximum. Useful for tallying expenses, quiz scores, inventory counts, and any situation requiring quick summation of a number list.
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Tip: For a quick sum of consecutive integers: sum = (first + last) × count / 2. Sum of 1 to 100: (1+100) × 100/2 = 5,050.
- 1Sum: add all numbers together (Σ = sum of all values)
- 2Count: number of values in the list
- 3Mean: Sum / Count
- 4Min/Max: smallest and largest values in the dataset
| Symbol | Meaning | Example |
|---|---|---|
| Σ | Sum of all values | Σ(1,2,3,4) = 10 |
| Σᵢ₌₁ⁿ xᵢ | Sum from i=1 to n | Σᵢ₌₁⁴ i = 1+2+3+4 = 10 |
| Σᵢ₌₁ⁿ i | Sum of first n integers | n(n+1)/2 → 1+2+...+100 = 5050 |
| Σᵢ₌₁ⁿ i² | Sum of squares | n(n+1)(2n+1)/6 |
| Σᵢ₌₁ⁿ i³ | Sum of cubes | (n(n+1)/2)² |
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Fun Fact
Carl Friedrich Gauss, aged 10, reportedly summed 1 to 100 instantly by noticing that 1+100=101, 2+99=101, and so on, making 50 pairs: 50×101=5,050. This elegant insight led to the formula n(n+1)/2.
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