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Basic Math/Calculating a weighted average.

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Expert: Josh - 7/2/2006


Question
I want to be reminded - from my distant statistics class - of how to calculate a weighted average of material received in a shipment made up of the following components:
40% of the items weigh 60 lbs.
25% weigh 45 lbs.
25% weigh 35 lbs.
10% weigh 90 lbs.
Thanks for your help with this.

Answer
Hi Ron,

In the context of your problem, the weights are essentially given by the percentages of each component.

The weighted average may be expressed as
W = a1*w1 + a2*w2 + a3*w3 + a4*w4,
where the scaling factors,
a1=0.40, a2=0.25, a3=0.25 and a4=0.10;
and the material (measured in pounds) are given by
w1=60, w2=45, w3=35 and s4=90, respectively.

Therefore, the weighted average,
W=0.4*60+0.25*45+0.25*35+0.1*90

Note: the "a"'s sum to one.

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Josh

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When I work through problems, I like to emphasize concepts which I believe are worth noting. I will try to answer questions in the following areas, but not at the advanced level. Algebra. Sequences & Series. Trigonometry. Functions & Graphs. Coordinate Geometry. Quadratic Polynomials. Exponential & Logarithms. Basic Calculus. Probability, Permutation and Combination. Mathematical Induction. Complex numbers. Physics problems.

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I have worked as a teaching assistant in college. My hope is that more people will share knowledge without boundary, give help without seeking recognition or monetary rewards.

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Bachelor degree in Engineering Science

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