GMAT Focus EditionData InsightsMedium
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 of 500 consumers, asking them to rate each brand on a scale of 1 to 5, where 1 is 'Poor' and 5 is 'Excellent'. The results are summarized in the table below: | Rating | Brand X | Brand Y | Brand Z | |---|---|---|---| | 1 (Poor) | 20 | 10 | 30 | | 2 | 40 | 30 | 50 | | 3 | 150 | 100 | 120 | | 4 | 180 | 200 | 150 | | 5 (Excellent) | 110 | 160 | 100 | Which brand has the highest average rating, and what is its approximate average rating?
- ABrand Y, 3.78
- BBrand X, 3.58
- CBrand Z, 3.44
- DBrand Y, 3.58
Show answer & explanationAnswer & explanation
Correct answer: A. Brand Y, 3.78
To find the average rating for each brand, multiply each rating by the number of consumers who gave that rating, sum these products, and then divide by the total number of consumers (500).
Why the other options are wrong
- B. Brand X's average rating is (1*20 + 2*40 + 3*150 + 4*180 + 5*110) / 500 = (20 + 80 + 450 + 720 + 550) / 500 = 1820 / 500 = 3.64. This option is incorrect.
- C. Brand Z's average rating is (1*30 + 2*50 + 3*120 + 4*150 + 5*100) / 500 = (30 + 100 + 360 + 600 + 500) / 500 = 1590 / 500 = 3.18. This option is incorrect.
- D. Brand Y's average rating is 3.94, not 3.58. This option is incorrect.
Weighted Average Calculation
A weighted average is an average in which each value contributes differently to the final average, based on a specific weight or frequency.
- Used when some data points are more important or occur more frequently than others.
- Calculated by summing the product of each value and its weight, then dividing by the sum of the weights.
- Common in statistics, finance, and survey analysis.
Memory trick: To find the true average, consider how much each part 'weighs' in.