Data and probability · Ages 14–15
Weighted mean worksheet
Part of: Measures of central tendency
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Weighted mean worksheet
Data and probability · Ages 14–15
Numsprite
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Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.A café's rating counts taste as 30% and service as 70%. It scores 87 for taste and 60 for service. What is its overall rating?
Answer:
2.A games review site rates a new game 69 for graphics, with weight 2, and 87 for gameplay, with weight 3. What is the weighted mean rating?
Answer:
3.A games review site rates a new game 85 for graphics, with weight 2, and 90 for gameplay, with weight 3. What is the weighted mean rating?
Answer:
4.A café's rating counts taste as 30% and service as 70%. It scores 74 for taste and 68 for service. What is its overall rating?
Answer:
5.A travel site rates a hotel 62 for location (weight 1), 67 for rooms (weight 2) and 79 for breakfast (weight 1). Σ(rating × weight) = , Σweights = , weighted mean = .
Fill in each blank
Answer:
6.A travel site rates a hotel 88 for location (weight 1), 61 for rooms (weight 3) and 66 for breakfast (weight 1). Σ(rating × weight) = , Σweights = , weighted mean = .
Fill in each blank
Answer:
7.An e-bike's rating is a weighted mean: range 72 (weight 3) and looks 74 (weight 2). The new model's range score is 3 higher than the old one's, its looks score the same. By how much is the new model's weighted mean higher?
Answer:
8.An e-bike's rating is a weighted mean: range 88 (weight 1) and looks 89 (weight 4). The new model's range score is 9 higher than the old one's, its looks score the same. By how much is the new model's weighted mean higher?
Answer:
Part B: Choose, or true or false (2 marks each)
9.In a review, a phone scores 58 for looks (weight 2) and 88 for performance (weight 4). What is its weighted mean score?
- A. 73
- B. 78
- C. 234
- D. 68
Choose the right answer
Answer:
10.In a review, a phone scores 68 for looks (weight 1) and 98 for performance (weight 3). What is its weighted mean score?
- A. 75.5
- B. 83
- C. 181
- D. 90.5
Choose the right answer
Answer:
11.In a diving contest, a dive's difficulty mark is 84 (weight 2) and its execution mark 87 (weight 3). Its weighted mean mark is 85.8.
True or false?
Answer:
12.In a diving contest, a dive's difficulty mark is 87 (weight 1) and its execution mark 81 (weight 2). Its weighted mean mark is 84.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.Two hotels on a travel site: hotel A scores 74 for location and 88 for breakfast; hotel B 84 and 67. The site's overall score gives location a weight of 3 and breakfast 1. Which hotel has the higher overall score?
- A. Only the plain means can tell
- B. They are equal
- C. Hotel A
- D. Hotel B
Choose the right answer
Working:
Answer:
14.A phone review site's overall score counts the camera as 20%, the battery 20% and the screen 60%. A phone scores 54, 89 and 77 for them. The three give , and points, and the overall score is .
Fill in each blank
Working:
Answer:
15.A platform's overall rating for a restaurant is a weighted mean of food (weight 1) and service (weight 1). A restaurant scores 90 for food. For an overall rating of 84, at least what must service score?
Working:
Answer:
16.A headphone review site used to take the plain mean of the sound and comfort scores as the overall score; now it uses a weighted mean, sound with weight 3 and comfort 1. A pair of headphones scores 93 for sound and 81 for comfort. The old overall score was , the new one is , higher.
Fill in each blank
Working:
Answer:
17.A platform's overall rating for a restaurant is a weighted mean of food (weight 1) and service (weight 2). A restaurant scores 80 for food. For an overall rating of 84, at least what must service score?
Working:
Answer:
18.Two hotels on a travel site: hotel A scores 87 for location and 83 for breakfast; hotel B 95 and 63. The site's overall score gives location a weight of 3 and breakfast 1. Which hotel has the higher overall score?
- A. Only the plain means can tell
- B. They are equal
- C. Hotel A
- D. Hotel B
Choose the right answer
Working:
Answer:
Show the answers and working
Weighted mean worksheet: Answers and working
Part A: Working out and filling in
1. 68.1 points
The weights are percentages making 100%, so no dividing: 87 × 30% + 60 × 70% = 68.1.
2. 79.8 points
Σ(rating × weight) ÷ Σweights = (69 × 2 + 87 × 3) ÷ (2 + 3) = 399 ÷ 5 = 79.8.
3. 88 points
Σ(rating × weight) ÷ Σweights = (85 × 2 + 90 × 3) ÷ (2 + 3) = 440 ÷ 5 = 88.
4. 69.8 points
The weights are percentages making 100%, so no dividing: 74 × 30% + 68 × 70% = 69.8.
5. 275, 4, 68.75
62 × 1 + 67 × 2 + 79 × 1 = 275; 1 + 2 + 1 = 4; 275 ÷ 4 = 68.75.
6. 337, 5, 67.4
88 × 1 + 61 × 3 + 66 × 1 = 337; 1 + 3 + 1 = 5; 337 ÷ 5 = 67.4.
7. 1.8 points
Only the range score changed, and it carries 3 ÷ (3 + 2) of the weight: the weighted mean rises by 3 × 3 ÷ 5 = 1.8 (working out both weighted means and subtracting gives the same).
8. 1.8 points
Only the range score changed, and it carries 1 ÷ (1 + 4) of the weight: the weighted mean rises by 9 × 1 ÷ 5 = 1.8 (working out both weighted means and subtracting gives the same).
Part B: Choose, or true or false
9. B. 78
(58 × 2 + 88 × 4) ÷ (2 + 4) = 468 ÷ 6 = 78, nearer the heavier 88 than the plain mean 73 is.
10. D. 90.5
(68 × 1 + 98 × 3) ÷ (1 + 3) = 362 ÷ 4 = 90.5, nearer the heavier 98 than the plain mean 83 is.
11. True
(84 × 2 + 87 × 3) ÷ (2 + 3) = 429 ÷ 5 = 85.8.
12. False
(87 × 1 + 81 × 2) ÷ (1 + 2) = 249 ÷ 3 = 83.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. D. Hotel B
A 77.5, B 79.75: location weighs more, so the better-placed hotel wins; the plain means would say the opposite.
14. 10.8, 17.8, 46.2, 74.8
54 × 20% = 10.8, 89 × 20% = 17.8, 77 × 60% = 46.2: 74.8 in all.
15. 78 points
(90 × 1 + y) ÷ 2 = 84: 90 + y = 168, y = 78.
16. 87, 90, 3
Before, (93 + 81) ÷ 2 = 87; now (93 × 3 + 81 × 1) ÷ (3 + 1) = 360 ÷ 4 = 90; 90 − 87 = 3 higher: the heavier sound score is the higher one, so the overall score rises.
17. 86 points
(80 × 1 + 2y) ÷ 3 = 84: 80 + 2y = 252, y = 86.
18. D. Hotel B
A 86, B 87: location weighs more, so the better-placed hotel wins; the plain means would say the opposite.
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