How this calculator works
The sum of products pairs the lists by position, multiplies each pair and adds every result. Order matters: the first value of one list pairs with the first value of the other, so rearranging one list changes the answer. The operation is the dot product of two vectors, and it appears throughout statistics and engineering. The mean product divides the total by the number of pairs.
Formula
For lists a and b of length n, the sum of products is a₁b₁ + a₂b₂ + ... + aₙbₙ. The mean product is that total divided by n.
Worked example
Pairing 2, 3 and 4 with 5, 6 and 7 gives 2 × 5 = 10, 3 × 6 = 18 and 4 × 7 = 28. The sum is 56 and the mean product is 56/3 ≈ 18.667.
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Frequently asked questions
How is this different from a weighted average?
A weighted average divides the sum of products by the sum of the weights. The sum of products stops one step earlier and reports the numerator alone. If the second list is a set of weights, divide by their total to get the weighted mean.
Can the lists have different lengths?
No, pairs must line up. If one list is longer, the extra values have no partner, so the calculator asks for equal lengths rather than silently ignoring them.
Do negative numbers work?
Yes. A negative value flips the sign of its product, and products can cancel, so the total may be smaller than any individual term or even zero.
What is this used for in statistics?
The sum of products of deviations from the means is the numerator of the correlation and covariance formulas. Because the deviations can be negative, that sum measures whether two variables move together or in opposite directions.