A restaurant collected ratings from 10 customers on a scale of 1 to 5. The resulting data is shown in the table below. What is the average rating if the metrics are combined with the weights food : ambience : service = 6 : 5 : 4?
Step-by-step solution
| 5★ | 4★ | 3★ | 2★ | 1★ | |
|---|---|---|---|---|---|
| Food | 5 | 3 | 2 | 0 | 0 |
| Ambience | 0 | 4 | 5 | 1 | 0 |
| Service | 1 | 2 | 2 | 4 | 1 |
To find: The weighted average rating
Idea: First find the average rating for each metric (each row is a frequency table of 10 ratings). Then combine the three averages with the weights 6, 5, 4.
- Food: 5 × 5 + 4 × 3 + 3 × 210 = 25 + 12 + 610 = 4.3.½ mark
- Ambience: 4 × 4 + 3 × 5 + 2 × 110 = 16 + 15 + 210 = 3.3.½ mark
- Service: 5 × 1 + 4 × 2 + 3 × 2 + 2 × 4 + 1 × 110 = 5 + 8 + 6 + 8 + 110 = 2.8.½ mark
- Weighted average = 6 × 4.3 + 5 × 3.3 + 4 × 2.86 + 5 + 4 = 25.8 + 16.5 + 11.215 = 53.515 ≈ 3.57.1½ marks
Check: Each row adds up to 10 customers ✓ (5 + 3 + 2, 4 + 5 + 1, 1 + 2 + 2 + 4 + 1). 3.57 lies between 2.8 and 4.3 and is pulled up by food, which has the largest weight ✓.
Answer to write in the exam
Food average = 25 + 12 + 610 = 4.3
Ambience average = 16 + 15 + 210 = 3.3
Service average = 5 + 8 + 6 + 8 + 110 = 2.8
Average rating = 6 × 4.3 + 5 × 3.3 + 4 × 2.86 + 5 + 4 = 53.515 = 3.57
∴ Average rating ≈ 3.57
Common mistakes that cost marks
- Averaging the numbers in the table (5, 3, 2, 0, 0) instead of the ratings. The table gives how many customers chose each star rating.
- Dividing each row by 5 (the number of columns) instead of by 10 customers.
- Taking a simple mean of 4.3, 3.3 and 2.8 (3.47) and ignoring the weights.
How this can come in the exam
A café’s average food rating is 4 and its average service rating is 3. With weights food : service = 3 : 1, the combined rating is
- 3.5
- 3.75
- 3.25
- 7
Show answer
(B) 3.75
3 × 4 + 1 × 34 = 154 = 3.75.
Try one yourself
Five customers rate a dish for taste as 5, 5, 4, 4, 2 and for price as 3, 3, 4, 2, 3. Combine taste and price with weights 3 : 2.
Show answer
Taste average = 4, price average = 3. Combined = 3 × 4 + 2 × 35 = 3.6.
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