Sum of Products Calculator
Calculate the sum of products for corresponding elements in datasets
Calculate Sum of Products
Sum of Products = Σ(aᵢ × bᵢ)
Multiply corresponding elements from two datasets and sum the results
Enter numbers separated by commas or spaces
Enter numbers separated by commas or spaces
Sum of Products Examples
Basic Example
Dataset A: [2, 4, 6]
Dataset B: [1, 3, 5]
Products: 2×1=2, 4×3=12, 6×5=30
Sum: 2+12+30 = 44
With Negative Numbers
Dataset A: [-2, 4, -6]
Dataset B: [3, -1, 2]
Products: -2×3=-6, 4×(-1)=-4, -6×2=-12
Sum: -6+(-4)+(-12) = -22
Formula
Two Datasets
∑(aᵢ × bᵢ)
Three Datasets
∑(aᵢ × bᵢ × cᵢ)
Applications
Statistics
Covariance calculations
Finance
Weighted cost calculations
Data Analysis
Correlation analysis
Engineering
Signal processing
Tips & Notes
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All datasets must have equal length
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Zero in any dataset makes that product zero
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Useful for weighted calculations
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Common in statistical analysis
Understanding Sum of Products
What is Sum of Products?
The sum of products is a mathematical operation that multiplies corresponding elements from two or more datasets and then adds up all the resulting products. This calculation is fundamental in statistics, data analysis, and many mathematical applications.
Calculation Steps
- 1. Identify the datasets to be used
- 2. Ensure all datasets have equal length
- 3. Multiply corresponding elements: a₁×b₁, a₂×b₂, etc.
- 4. Sum all the products to get the final result
Mathematical Formula
For two datasets:
∑(aᵢ × bᵢ) = a₁×b₁ + a₂×b₂ + ... + aₙ×bₙ
Real-World Applications
- •Statistics: Calculating covariance and correlation
- •Finance: Weighted average cost of capital (WACC)
- •Physics: Dot product calculations
- •Machine Learning: Feature weighting