Weighted Averages AMDM NIX

Front

What is a weighted average?

Back

A weighted average is a calculation that takes into account the importance or weight of each value being averaged.

Front

How do you calculate a weighted average?

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Multiply each value by its corresponding weight, sum up the results, and then divide by the sum of the weights.

Front

What is the formula for calculating a weighted average?

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Weighted Average = (Σ(value × weight)) / Σ(weight) where Σ denotes the sum.

Front

What is the significance of weights in a weighted average?

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Weights determine the relative importance of each value in the average calculation.

Front

If a student scores 70% on a test worth 50% and 90% on a quiz worth 50%, what is their weighted average?

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Weighted Average = (70% × 0.5) + (90% × 0.5) = 80%.

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In a weighted average, what happens if one value has a much higher weight than others?

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The weighted average will be closer to the value with the higher weight.

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How does a weighted average differ from a simple average?

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A simple average treats all values equally, while a weighted average accounts for the importance of each value.

Front

What is the weighted average price of shirts if 50 small shirts ($10), 30 medium shirts ($15), and 20 large shirts ($20) are sold?

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Weighted Average Price = ($10×50 + $15×30 + $20×20) / (50 + 30 + 20) = $13.33.

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If a company sells 10 units of product A ($1000), 20 units of product B ($2000), and 15 units of product C ($3000), what is the weighted average sales revenue?

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Weighted Average Revenue = ($1000×10 + $2000×20 + $3000×15) / (10 + 20 + 15) = $2250.

Front

What is the weighted average of a student's scores if tests are 40%, quizzes 30%, and homework 30% with scores of 80%, 90%, and 95% respectively?

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Weighted Average = (80%×0.4) + (90%×0.3) + (95%×0.3) = 87.5%.