Combined Mean - Worksheets, Questions and Revision

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GCSE · Statistics

S09 Combined Mean

EDEXCEL 1ST0 · Calculator allowed · about 80 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A fitness app records the number of press-ups done by two groups of members in one week.

Group A: 6 members, mean of 14 press-ups each.
Group B: 4 members, mean of 9 press-ups each.

Work out the combined mean number of press-ups per member, for all 10 members.

(Total for Question 1 is 3 marks)

20 pupils took a spelling test.

Class 7X: 8 pupils, mean score 6.
Class 7Y: 12 pupils, mean score 9.

Work out the combined mean spelling score of all 20 pupils.

(Total for Question 2 is 3 marks)

The mean height of 5 plants in tray A is 18 cm. The mean height of 5 plants in tray B is 24 cm.

Work out the combined mean height of all 10 plants.

(Total for Question 3 is 2 marks)

The mean number of goals scored by 9 players in a football squad is 5. A new player joins the squad having scored 15 goals this season.

Work out the new mean number of goals scored per player, for all 10 players.

(Total for Question 4 is 3 marks)

For each statement about combined means, write down whether it is True or False.

(i)If two groups are exactly the same size, the combined mean is the mean of the two individual means.(1)

(ii)The combined mean of two groups is always exactly halfway between the two individual means, whatever the group sizes.(1)

(iii)A larger group has a bigger effect on the combined mean than a smaller group.(1)

(iv)If one of the two groups has 0 members, the combined mean equals the mean of the other group.(1)

(Total for Question 5 is 4 marks)

A bakery sells loaves at two branches on Saturday.

Branch 1: 12 loaves sold, mean price £2.40 each.
Branch 2: 8 loaves sold, mean price £3.15 each.

Work out the combined mean price of all 20 loaves sold.

(Total for Question 6 is 3 marks)

The mean mass of 11 parcels is 4 kg. A 12th parcel is added and the mean mass of all 12 parcels becomes 4.5 kg.

Work out the mass of the 12th parcel.

(Total for Question 7 is 4 marks)

Three classes sit the same maths test.

Class X: 25 pupils, mean score 62.
Class Y: 20 pupils, mean score 70.
Class Z: 15 pupils, mean score 58.

Work out the combined mean score of all 60 pupils.

(Total for Question 8 is 5 marks)

The mean of 8 numbers is 15. One of the numbers, 23, is removed.

Work out the mean of the remaining 7 numbers.

(Total for Question 9 is 4 marks)

The mean weekly wage of 12 employees in a small office is £480. The manager, whose wage is £660, then leaves the company.

Work out the mean weekly wage of the remaining 11 employees.

(Total for Question 10 is 4 marks)

Two groups of runners took part in a relay event.

Group P has 10 runners with a mean time of 48 seconds.
Group Q has 15 runners.
The combined mean time for all 25 runners is 52 seconds.

Work out the mean time for Group Q.

(Total for Question 11 is 4 marks)

A shop sells two brands of coffee.

Brand A: 30 bags sold, mean price £4.00 per bag.
Brand B: n bags sold, mean price £6.00 per bag.
The combined mean price for all bags sold is £5.00.

Work out the value of n.

(Total for Question 12 is 5 marks)

A gym has two branches.

Branch North: 45 members, mean of 12 visits per member last month.
Branch South: 55 members, mean of 9 visits per member last month.

(a)Work out the combined mean number of visits per member per month across both branches.(3)

(b)The gym manager claims: 'The combined mean is exactly halfway between 12 and 9.' Use your answer to part (a) to assess whether the manager is correct.(2)

(Total for Question 13 is 5 marks)

Four youth clubs recorded the mean number of hours their members volunteered last month.

Club	Members	Mean hours
Riverside	22	6
Oakfield	18	9
Brookside	25	5
Hillside	15	11

Work out the combined mean number of volunteering hours per member across all four clubs.

(Total for Question 14 is 4 marks)

A school wants to estimate the combined mean number of books read per pupil over the summer, across the whole of Year 8 (120 pupils in 4 tutor groups).

(a)Before collecting the data, write down one decision the school should make so that the data collected from each tutor group can be fairly combined.(1)

(b)Each tutor group's mean number of books read is recorded below.

Tutor group	Number of pupils	Mean books read
8A	28	5
8B	32	4
8C	30	6
8D	30	7

Work out the combined mean number of books read per pupil across all of Year 8.(4)

(c)A tutor claims: 'More than half of the tutor groups read above the whole-year average.' Use the table and your answer to part (b) to assess whether this claim is correct.(2)

(d)Give one reason why the school should be cautious about using this combined mean to describe how much all pupils nationally read over the summer.(1)

(Total for Question 15 is 8 marks)

Three warehouses store boxes of a product.

Warehouse 1: 50 boxes, mean weight 12 kg.
Warehouse 2: 30 boxes, mean weight 15 kg.
Warehouse 3: 20 boxes, mean weight w kg.

The combined mean weight of all 100 boxes is 13.4 kg.

Work out the value of w.

(Total for Question 16 is 5 marks)

Group A has a members with mean p. Group B has b members with mean q, where a is not equal to b.

Explain why the combined mean of the two groups is not, in general, equal to (p+q) / 2 unless a = b.

(Total for Question 17 is 3 marks)

A sample of 15 lightbulbs has a mean lifetime of 800 hours.

(a)A 16th lightbulb, with a lifetime of 970 hours, is added to the sample. Work out the new mean lifetime of all 16 lightbulbs.(3)

(b)One faulty lightbulb from the original 15, with a lifetime of 350 hours, is then removed from the 16-bulb sample. Work out the mean lifetime of the remaining 15 lightbulbs.(3)

(Total for Question 18 is 6 marks)

A company has three sales teams.

Team 1: 12 staff, mean sales £4200 per person.
Team 2: 18 staff, mean sales £3600 per person.
Team 3: t staff, mean sales £5000 per person.

The combined mean sales per person across all three teams is £4400.

(a)Show that the total sales for Team 1 and Team 2 combined is £115 200.(3)

(b)Find the value of t.(4)

(c)The company states: 'Team 3 is the largest team.' Use your answer to part (b) to assess whether this statement is correct.(1)

(Total for Question 19 is 8 marks)

Mark scheme · S09 Combined Mean

Question 1

M1 6x14 + 4x9 ( = 120), oe (total press-ups for all 10 members)
M1 120 / 10 (dep on M1)
A1 12 cao
Answer: 12

Question 2

M1 8x6 + 12x9 ( = 156), oe (total score for all 20 pupils)
M1 156 / 20 (dep on M1)
A1 7.8 cao
Answer: 7.8

Question 3

M1 (5x18 + 5x24) / 10, oe
A1 21 cm cao
Answer: 21 cm

Question 4

M1 9x5 ( = 45), oe (original total goals)
M1 (45 + 15) / 10 (dep on M1)
A1 6 cao
Answer: 6

Question 5

(i) B1 True cao
(i) Answer: True
(ii) B1 False cao
(ii) Answer: False
(iii) B1 True cao
(iii) Answer: True
(iv) B1 True cao
(iv) Answer: True

Question 6

M1 12x2.40 + 8x3.15 ( = 54.00), oe (total takings for all 20 loaves)
M1 54.00 / 20 (dep on M1)
A1 £2.70 cao
Answer: £2.70

Question 7

M1 11x4 ( = 44), oe (original total mass)
M1 12x4.5 ( = 54), oe (new total mass)
M1 54 - 44 (dep on both previous method marks)
A1 10 kg cao
Answer: 10 kg

Question 8

M1 25x62 ( = 1550), oe
M1 20x70 ( = 1400), oe
M1 15x58 ( = 870), oe
M1 (1550+1400+870) / 60 (dep on previous three method marks)
A1 awrt 63.7 cao
Answer: awrt 63.7

Question 9

M1 8x15 ( = 120), oe
M1 120 - 23 ( = 97), oe (dep)
M1 97 / 7 (dep)
A1 awrt 13.9 cao
Answer: awrt 13.9

Question 10

M1 12x480 ( = 5760), oe
M1 5760 - 660 ( = 5100), oe (dep)
M1 5100 / 11 (dep)
A1 awrt £463.64 cao
Answer: awrt £463.64

Question 11

M1 25x52 ( = 1300), oe (total time for all 25 runners)
M1 10x48 ( = 480), oe (total time for Group P)
M1 1300 - 480 ( = 820), oe (dep, total time for Group Q)
A1 820 / 15 = awrt 54.7 seconds cao
Answer: awrt 54.7 seconds

Question 12

M1 30x4 ( = 120), oe (total for Brand A)
M1 sets up (120 + 6n) / (30+n) = 5, oe
M1 120 + 6n = 5(30+n) ( = 150+5n), oe
M1 6n - 5n = 150 - 120 (dep, = 30)
A1 n = 30 cao
Answer: n = 30

Question 13

(a) M1 45x12 + 55x9 ( = 1035), oe (total visits across both branches)
(a) M1 1035 / 100 (dep on M1)
(a) A1 10.35 cao
(a) Answer: 10.35
(b) B1 No, the manager is not correct cao
(b) B1 reason: halfway between 12 and 9 is 10.5, but the combined mean is 10.35; because Branch South (55 members) is larger than Branch North (45 members), the combined mean is pulled closer to South's mean of 9, oe
(b) Answer: No; halfway between 12 and 9 is 10.5, but the combined mean is 10.35, because the larger branch (South, 55 members) pulls the mean towards its own mean of 9.

Question 14

M1 22x6 + 18x9 + 25x5 + 15x11 ( = 584), oe (total hours across all four clubs)
M1 22+18+25+15 ( = 80), oe (total number of members)
M1 584 / 80 (dep on both previous method marks)
A1 7.3 hours cao
Answer: 7.3 hours

Question 15

(a) B1 any sensible planning decision, e.g. using the same time period and the same definition of 'a book read' for every tutor group, oe
(a) Answer: e.g. Use the same time period (the whole summer holiday) and the same definition of 'a book read' for every tutor group.
(b) M1 28x5 + 32x4 + 30x6 + 30x7 ( = 658), oe (total books read)
(b) M1 28+32+30+30 ( = 120), oe (total pupils)
(b) M1 658 / 120 (dep on both previous method marks)
(b) A1 awrt 5.48 cao
(b) Answer: awrt 5.48
(c) B1 the claim is not correct (False) cao
(c) B1 reason: only 8C (6) and 8D (7) have means above 5.48, which is 2 out of 4 tutor groups, exactly half rather than more than half, oe
(c) Answer: No; only 8C and 8D (2 of the 4 tutor groups) have a mean above 5.48, which is exactly half, not more than half.
(d) B1 the data comes from only one school, so may not be representative of pupils nationally, oe
(d) Answer: The sample is only from one school (one Year 8 cohort), so it may not represent pupils nationally.

Question 16

M1 100x13.4 ( = 1340), oe (total weight of all 100 boxes)
M1 50x12 ( = 600), oe (total weight, Warehouse 1)
M1 30x15 ( = 450), oe (total weight, Warehouse 2)
M1 1340 - 600 - 450 ( = 290), oe (dep on all previous method marks)
A1 290 / 20 = 14.5 kg cao
Answer: 14.5 kg

Question 17

B1 combined mean = (ap + bq) / (a+b), oe (correct weighted formula stated)
B1 (p+q)/2 treats both groups as equally weighted, which is only valid when a = b, oe
B1 since a is not equal to b, the larger group contributes more to the total, so the combined mean is pulled towards the mean of the larger group and is generally not equal to (p+q)/2, oe
Answer: The combined mean is (ap+bq)/(a+b), which only simplifies to (p+q)/2 when a=b; since a is not equal to b, the larger group has more influence, pulling the combined mean towards its own mean.

Question 18

(a) M1 15x800 ( = 12000), oe (original total lifetime)
(a) M1 (12000 + 970) / 16 (dep on M1)
(a) A1 810.625 hours cao
(a) Answer: 810.625 hours
(b) M1 12970 - 350 ( = 12620), oe
(b) M1 12620 / 15 (dep)
(b) A1 awrt 841.3 hours cao
(b) Answer: awrt 841.3 hours

Question 19

(a) M1 12x4200 ( = 50400), oe (total sales, Team 1)
(a) M1 18x3600 ( = 64800), oe (total sales, Team 2)
(a) A1 50400 + 64800 = 115 200 shown
(a) Answer: £115 200 (shown)
(b) M1 115200 + 5000t, oe (total sales for all staff)
(b) M1 4400 x (30+t), oe ( = 132000 + 4400t)
(b) M1 5000t - 4400t = 132000 - 115200, oe ( = 600t = 16800)
(b) A1 t = 28 cao
(b) Answer: t = 28
(c) B1 correct (True), since Team 3 has 28 staff, more than Team 2 (18) and Team 1 (12), oe
(c) Answer: Correct; Team 3 has 28 staff, which is more than Team 2 (18) and Team 1 (12).

Question 19

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Combined Mean - Worksheets, Questions and Revision

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S09 Combined Mean

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Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

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Question 19