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⚖️ Weighted Average Calculator

Enter values and their weights (e.g. exam scores with credit hours). Each row = one value + its weight.

📐 Statistical Formulas

Mean (Arithmetic Average)

Sum of all values divided by the count of values.

Mean (x̄) = Σx / n

Example: [2, 4, 6, 8, 10]
= (2+4+6+8+10) / 5 = 30/5 = 6

Median

Middle value when sorted. If even count, average the two middle values.

Odd count: median = middle value
Even count: median = (middle1 + middle2) / 2

Example (odd): [2,4,6,8,10] → median = 6
Example (even): [2,4,6,8] → median = (4+6)/2 = 5

Mode

Value(s) that appear most frequently. Can have multiple modes.

Example: [2,3,3,4,5,5,5] → mode = 5
Example: [1,1,2,2,3] → modes = 1 and 2 (bimodal)
Example: [1,2,3,4] → no mode (all equal frequency)

Standard Deviation

Measures how spread out the numbers are from the mean.

Population σ = √(Σ(x - x̄)² / n)
Sample s = √(Σ(x - x̄)² / (n-1))

Steps:
1. Find mean x̄
2. Subtract mean from each value: (x - x̄)
3. Square each: (x - x̄)²
4. Average the squares (variance)
5. Take square root

Weighted Average

Weighted Mean = Σ(value × weight) / Σ(weights)

Example: Exam 80 (weight 3) + Quiz 90 (weight 1)
= (80×3 + 90×1) / (3+1)
= (240 + 90) / 4 = 330/4 = 82.5

Geometric & Harmonic Mean

Geometric Mean = ⁿ√(x₁ × x₂ × ... × xₙ)
→ Use for: growth rates, ratios, percentages

Harmonic Mean = n / Σ(1/xᵢ)
→ Use for: speeds, rates, densities

Quartiles & IQR

Q1 = 25th percentile (median of lower half)
Q2 = 50th percentile (median)
Q3 = 75th percentile (median of upper half)
IQR = Q3 - Q1 (Interquartile Range)

Outlier if: x < Q1 - 1.5×IQR
or: x > Q3 + 1.5×IQR

❓ Frequently Asked Questions

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