Data and probability · Ages 14–15

Weighted mean word problems worksheet

Part of: Measures of central tendency

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Data and probability · Ages 14–15

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.Group A's 4 people folded 11 paper cranes each on average, and group B's 2 people 6 each. How many cranes did the two groups fold in all?
Answer:
2.Team A's 21 people have a mean weight of 43 kg and team B's 14 people 59 kg. What is the mean weight of the two teams together, in kg?
Answer:
3.Group A's 6 people folded 7 paper cranes each on average, and group B's 4 people 3 each. How many cranes did the two groups fold in all?
Answer:
4.A running club's 38 members ran 58 km each on average last week. Its 19 men averaged 49 km. How many km did its 19 women average?
Answer:
5.Fleet A's 16 vans have a mean age of 24 months and fleet B's 47 months. Together their mean age is 39 months. How many vans are in fleet B?
Answer:
6.A running club's 36 members ran 59 km each on average last week. Its 18 men averaged 45 km. How many km did its 18 women average?
Answer:
7.In a dance troupe the numbers of men and women are in the ratio 3 : 2; the men's mean height is 172 cm and the women's 153 cm. What is the whole troupe's mean height, in cm?
Answer:
8.In a dance troupe the numbers of men and women are in the ratio 3 : 1; the men's mean height is 168 cm and the women's 158 cm. What is the whole troupe's mean height, in cm?
Answer:

9.27 morning customers spent $55 each on average and 18 afternoon customers $73. What did a customer spend on average all day?
- A. $62.2
- B. $64
- C. $1,399.5
- D. $65.8
Choose the right answer
Answer:
10.30 morning customers spent $58 each on average and 15 afternoon customers $64. What did a customer spend on average all day?
- A. $61
- B. $60
- C. $62
- D. $1,350
Choose the right answer
Answer:
11.Group A's 12 people take 54 minutes on average to finish a jigsaw and group B's 12 people 70 minutes. The two groups' combined mean time is exactly the mean of 54 and 70.
True or false?
Answer:
12.Group A's 17 people take 50 minutes on average to finish a jigsaw and group B's 27 people 66 minutes. The two groups' combined mean time is exactly the mean of 50 and 66.
True or false?
Answer:

13.A tour travels in three coaches: the first has 15 people averaging 27 years old, the second 5 averaging 39, the third 7 averaging 30. Their ages add up to years, there are people, and the mean age is .
Fill in each blank
Working:
Answer:
14.A go club's 42 members have a mean age of 32. 6 new members averaging 22 years old join. What is the club's mean age now?
Working:
Answer:
15.A sports club's volleyball team has 22 players averaging 165 cm and its basketball team 38 averaging 159 cm. The volleyball team's heights add up to cm, the basketball team's cm, and the mean height of both teams is cm.
Fill in each blank
Working:
Answer:
16.A bookshop had 28 customers on Saturday, spending $36 each on average; Sunday's customers spent $50 each on average. Over the two days the mean was $43. How many customers came on Sunday?
Working:
Answer:
17.A tour travels in three coaches: the first has 18 people averaging 22 years old, the second 10 averaging 38, the third 12 averaging 32. Their ages add up to years, there are people, and the mean age is .
Fill in each blank
Working:
Answer:
18.A bookshop had 12 customers on Saturday, spending $38 each on average; Sunday's customers spent $61 each on average. Over the two days the mean was $49. How many customers came on Sunday?
Working:
Answer:

Show the answers and working

Weighted mean word problems worksheet: Answers and working

1. 56 cranes
Each group's total = its size × its mean: 4 × 11 = 44 and 2 × 6 = 12, so 44 + 12 = 56 in all.
2. 49.4 kg
Weight by the team sizes: (21 × 43 + 14 × 59) ÷ (21 + 14) = 1729 ÷ 35 = 49.4 kg.
3. 54 cranes
Each group's total = its size × its mean: 6 × 7 = 42 and 4 × 3 = 12, so 42 + 12 = 54 in all.
4. 67 km
In all 38 × 58 = 2204 km, the men 19 × 49 = 931 km, so the women (2204 − 931) ÷ 19 = 67 km.
5. 30 vans
Say fleet B has y: 16 × 24 + 47y = 39(16 + y), so 16 × (39 − 24) = y × (47 − 39): y = 30.
6. 73 km
In all 36 × 59 = 2124 km, the men 18 × 45 = 810 km, so the women (2124 − 810) ÷ 18 = 73 km.
7. 164.4 cm
The actual numbers aren't needed: the men are 3 parts and the women 2, so weight by the parts: (3 × 172 + 2 × 153) ÷ (3 + 2) = 822 ÷ 5 = 164.4 cm.
8. 165.5 cm
The actual numbers aren't needed: the men are 3 parts and the women 1, so weight by the parts: (3 × 168 + 1 × 158) ÷ (3 + 1) = 662 ÷ 4 = 165.5 cm.

9. A. $62.2
(27 × 55 + 18 × 73) ÷ (27 + 18) = 62.2: weighted by the numbers of customers.
10. B. $60
(30 × 58 + 15 × 64) ÷ (30 + 15) = 60: weighted by the numbers of customers.
11. True
Combined mean = (12 × 54 + 12 × 70) ÷ (12 + 12) = 62; only with equal groups is it (54 + 70) ÷ 2 = 62.
12. False
Combined mean = (17 × 50 + 27 × 66) ÷ (17 + 27) = 65811; only with equal groups is it (50 + 66) ÷ 2 = 58.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 810, 27, 30
15 × 27 + 5 × 39 + 7 × 30 = 810; 15 + 5 + 7 = 27; 810 ÷ 27 = 30.
14. 30.75 years
(42 × 32 + 6 × 22) ÷ (42 + 6) = 30.75.
15. 3630, 6042, 161.2
22 × 165 = 3630, 38 × 159 = 6042, (3630 + 6042) ÷ 60 = 161.2 cm.
16. 28 customers
Say y came on Sunday: 28 × 36 + 50y = 43(28 + y), so 28 × (43 − 36) = y × (50 − 43): y = 28.
17. 1160, 40, 29
18 × 22 + 10 × 38 + 12 × 32 = 1160; 18 + 10 + 12 = 40; 1160 ÷ 40 = 29.
18. 11 customers
Say y came on Sunday: 12 × 38 + 61y = 49(12 + y), so 12 × (49 − 38) = y × (61 − 49): y = 11.

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