The mean number of laps swum by 6 swimmers in a training session is 8. Work out the total number of laps swum by the 6 swimmers.
(Total for Question 1 is 1 mark)
2
The total mass of 5 parcels is 40 kg. Work out the mean mass of the 5 parcels.
(Total for Question 2 is 1 mark)
3
Group A has 4 members with a mean score of 15. Group B has 6 members with a mean score of 15. Write down the combined mean score of all 10 members, without calculating.
(Total for Question 3 is 1 mark)
4
Write down whether the following statement is True or False. The combined mean of two groups is always exactly halfway between the two individual means.
(Total for Question 4 is 1 mark)
5
The mean number of press-ups done by 8 members of Group P in one session is 20. The mean number of press-ups done by 12 members of Group Q is 25. Work out the total number of press-ups done by all 20 members.
(Total for Question 5 is 2 marks)
6
12 pupils in Class 7X have a mean spelling score of 6. 18 pupils in Class 7Y have a mean spelling score of 9. Work out the combined mean score for all 30 pupils.
(Total for Question 6 is 2 marks)
7
The mean height of 6 plants in Tray A is 20 cm. The mean height of 9 plants in Tray B is 25 cm. Work out the combined mean height of all 15 plants.
(Total for Question 7 is 2 marks)
8
The mean number of goals scored by 10 players in a hockey squad is 4. A new player joins the squad having scored 15 goals so far this season. Work out the new mean number of goals for all 11 players.
(Total for Question 8 is 2 marks)
9
The mean mass of 9 boxes is 6 kg. A 10th box is added and the mean mass of all 10 boxes becomes 6.8 kg. Work out the mass of the 10th box.
(Total for Question 9 is 2 marks)
10
The mean of 7 numbers is 12. One of the numbers, 19, is removed. Work out the mean of the remaining 6 numbers.
(Total for Question 10 is 2 marks)
11
A shop sells two brands of tea. Brand A: 40 boxes sold, mean price 3.20 pounds per box. Brand B: 25 boxes sold, mean price 4.00 pounds per box. Work out the combined mean price per box for all 65 boxes sold.
(Total for Question 11 is 2 marks)
12
Group A has 5 members with a mean age of 30. Group B has 5 members with a mean age of 40. Write down the combined mean age of all 10 members, without full working, using the fact the groups are equal in size.
(Total for Question 12 is 1 mark)
13
Write down whether the following statement is True or False. If a new value is added to a data set and that value is greater than the current mean, the new mean must be greater than the old mean.
(Total for Question 13 is 1 mark)
14
Two youth clubs recorded the mean number of hours volunteered last month. Club 1: 10 members, mean 6 hours. Club 2: 15 members, mean 8 hours. Work out the combined mean number of hours volunteered across both clubs.
(Total for Question 14 is 2 marks)
15
Three classes sit the same maths test. Class X: 20 pupils, mean score 58. Class Y: 25 pupils, mean score 66. Class Z: 15 pupils, mean score 70. (a) Work out the total score for all three classes combined. (b) Work out the combined mean score for all 60 pupils.
(Total for Question 15 is 3 marks)
16
The mean weekly wage of 15 employees in a small office is 520 pounds. The manager, whose wage is 1240 pounds per week, is not included in this figure. Work out the mean weekly wage of all 16 people, including the manager.
(Total for Question 16 is 3 marks)
17
Two groups of runners took part in a relay event. Group P has 8 runners with a mean time of 52 seconds per leg. Group Q has 12 runners with a mean time of 58 seconds per leg. (a) Work out the total time for each group. (b) Work out the combined mean time per leg across all 20 runners.
(Total for Question 17 is 3 marks)
18
Group A has a members with a mean of p. Group B has b members with a mean of q, where a is not equal to b. Write down, in terms of a, b, p and q, an expression for the combined mean of both groups.
(Total for Question 18 is 3 marks)
19
A sample of 20 lightbulbs has a mean lifetime of 850 hours. A second sample of 30 lightbulbs from a different batch has a mean lifetime of 900 hours. (a) Work out the combined mean lifetime of all 50 lightbulbs. (b) One further lightbulb, with a lifetime of 700 hours, is added to the combined sample. Work out the new combined mean for all 51 lightbulbs.
(Total for Question 19 is 3 marks)
20
A company has three sales teams. Team 1: 10 staff, mean sales 3800 pounds per person. Team 2: 15 staff, mean sales 4200 pounds per person. Team 3: 25 staff, mean sales 4600 pounds per person. (a) Work out the total sales for all three teams combined. (b) Work out the combined mean sales per person across all 50 staff.
(Total for Question 20 is 3 marks)
Mark scheme · S09D Combined Mean: Fluency and Exam Drill
Question 1
B1 48 cao
Answer: 48
Question 2
B1 8 kg cao
Answer: 8 kg
Question 3
B1 15 cao
Answer: 15
Question 4
B1 False cao
Answer: False
Question 5
M1 correct method, (8x20) + (12x25)
A1 460 cao
Answer: 460
Question 6
M1 correct method, ((12x6)+(18x9))/30
A1 7.8 cao
Answer: 7.8
Question 7
M1 correct method, ((6x20)+(9x25))/15
A1 23 cao
Answer: 23
Question 8
M1 correct method, ((10x4)+15)/11
A1 5 cao
Answer: 5
Question 9
M1 correct method, (6.8x10) - (6x9)
A1 14 kg cao
Answer: 14 kg
Question 10
M1 correct method, ((7x12)-19)/6
A1 10.833... or 65/6, awrt 10.83 cao
Answer: 65/6 = 10.83 (2 dp)
Question 11
M1 correct method, ((40x3.20)+(25x4.00))/65
A1 3.51 (2 dp) cao
Answer: 3.51 pounds (2 dp)
Question 12
B1 35 cao
Answer: 35
Question 13
B1 True cao
Answer: True
Question 14
M1 correct method, ((10x6)+(15x8))/25
A1 7.2 cao
Answer: 7.2
Question 15
M1 correct method, (20x58)+(25x66)+(15x70)
A1 3860 cao
B1 64.33 (2 dp) or 3860/60, correctly following through
Answer: (a) 3860. (b) 64.33 (2 dp)
Question 16
M1 correct method, 15x520
M1 correct method, (7800+1240)/16
A1 565 cao
Answer: 565 pounds
Question 17
M1 correct method, (8x52) and (12x58)
A1 416 seconds and 696 seconds, both cao
B1 combined mean 55.6 seconds correctly following through
Answer: (a) Group P: 416 seconds; Group Q: 696 seconds. (b) 55.6 seconds
Question 18
M1 recognises total for A is a x p and total for B is b x q
M1 recognises combined total is divided by combined number of members, a + b