GMAT Focus EditionData InsightsHard
A market research firm is analyzing consumer preferences for three competing brands of coffee: Brand X, Brand Y, and Brand Z. They conducted a survey where respondents rated each brand on a scale of 1 to 5 (1=poor, 5=excellent) across three attributes: Flavor, Aroma, and Packaging. The firm wants to calculate a weighted average score for each brand, given the following weights for attributes: Flavor: 50% Aroma: 30% Packaging: 20% The average ratings for each brand are: Brand X: Flavor = 4.5, Aroma = 3.8, Packaging = 4.2 Brand Y: Flavor = 4.0, Aroma = 4.5, Packaging = 3.5 Brand Z: Flavor = 4.8, Aroma = 3.5, Packaging = 3.0 Which brand has the highest weighted average score?
- ABrand X
- BBrand Y
- CBrands X and Z have the same weighted average score.
- DBrand Z
Show answer & explanationAnswer & explanation
Correct answer: A. Brand X
To calculate the weighted average score, multiply each attribute's rating by its corresponding weight and sum the products. Brand X: (4.5 * 0.50) + (3.8 * 0.30) + (4.2 * 0.20) = 2.25 + 1.14 + 0.84 = 4.23. Brand Y: (4.0 * 0.50) + (4.5 * 0.30) + (3.5 * 0.20) = 2.00 + 1.35 + 0.70 = 4.05. Brand Z: (4.8 * 0.50) + (3.5 * 0.30) + (3.0 * 0.20) = 2.40 + 1.05 + 0.60 = 4.05. Brand X has the highest weighted average score of 4.23.
Why the other options are wrong
- B. Brand Y has a weighted average score of 4.05.
- C. Brands Y and Z have the same weighted average score, but Brand X is higher.
- D. Brand Z has a weighted average score of 4.05.
Weighted Average
A weighted average is an average that takes into account the varying degrees of importance or frequency of the numbers in a data set.
- Each value is multiplied by its weight before summing.
- The sum of weights must equal 1 (or 100%).
- Used when some data points contribute more than others to the overall average.
Memory trick: Value times Weight, then sum all right!