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Reverse mean Quiz

Grade 4 • 4X • 10 Questions (36 Marks)

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Reverse mean — Notes & Worked Examples Show / Hide

Explanation:

Because Mean = Total of ValuesNumber of Values, you can rearrange this formula to find the total of any group whenever you are given its mean: Total = Mean × Number of Values.

In any reverse mean or combined mean question, your very first step should always be to multiply each given mean by the number of items to find the totals, then add or subtract the totals as required.

Example 1: The mean mass of 5 parcels is 14 kg. When a 6th parcel is added, the mean of all 6 parcels becomes 15.5 kg. Find the mass of the 6th parcel.

Solution:

Total of 5 parcels = 5 × 14 = 70 kg
Total of 6 parcels = 6 × 15.5 = 93 kg
Mass of 6th parcel = 93 − 70 = 23 kg
Answer: 23 kg

Example 2: In a class, 12 boys have a mean score of 65 and 18 girls have a mean score of 70. Work out the mean score for all 30 students.

Solution:

Boys total = 12 × 65 = 780
Girls total = 18 × 70 = 1260
Combined total = 780 + 1260 = 2040
Overall mean = 2040 ÷ 30 = 68 → Answer: 68
Question 1
[1 mark]
The mean of five numbers is 5
Four of the numbers are 5, 2, 7, 3
Find the missing number
Worked Solution & Answer
Mean = total of all valuesnumber of values
8
Answer: 8
Question 2
[1 mark]
The mean weight of 8 boxes is 57 kg.
One box is removed and the mean weight decreases to 54 kg.
Work out the weight of the removed box.
kg
Worked Solution & Answer
Mean = total of all valuesnumber of values
78 kg
Answer: 78 kg kg
Question 3 IGCSE Jan 2022 2FR Q25
[3 marks]
A scientist is investigating the weight of 50 tigers.
Here is some information about these tigers.
Type of tigerSiberianBengalNumber of tigers2228Mean weight of tigers (kg)260
The mean weight of all 50 tigers is 218 kg
Work out the mean weight of the Bengal tigers.
kg
Worked Solution & Answer
Total weight of 50 tigers = 50 × 218 = 10 900 kg M1
Total weight of 22 Siberian tigers = 22 × 260 = 5720 kg M1
Bengal mean = (10 900 – 5720) ÷ 28 = 5180 ÷ 28 = 185 kg. A1
Answer: 185 kg
Question Paper (PDF) • Mark Scheme (PDF)
Question 4 AQA Jun 2022 3F Q14
[4 marks]
20 students are asked how many video games they played last month.
The chart shows information about the results.
01234567812345Number of studentsNumber of games
(a) How many students played more than 2 games? [1 mark]
Answer
(b) Work out the mean number of games played.
Give your answer as a decimal. [3 marks]
Answer
Worked Solution & Answer
(a)
Students who played 3, 4, or 5 games: 4 + 1 + 3 = 8. B1
Answer (a): Answer 8
(b)
(Mean = total of values ÷ number of values)
Total games = (1 × 7) + (2 × 5) + (3 × 4) + (4 × 1) + (5 × 3) M1
= 7 + 10 + 12 + 4 + 15 = 48. M1
Mean = 4820 = 2.4. A1
Answer (b): Answer 2.4
Question Paper (PDF) • Mark Scheme (PDF)
Question 5 IGCSE Jun 2022 1F Q12
[4 marks]
The table gives information about the number of gold stars won by each of 25 students in class 7T last week.
Number of gold starsNumber of students0615243743
(a) Work out the mean number of gold stars won. [3 marks]
(b) Work out the probability that this student did **not** win at least one gold star last week. [1 mark]
Worked Solution & Answer
(a)
Total stars = (0×6) + (1×5) + (2×4) + (3×7) + (4×3) = 0 + 5 + 8 + 21 + 12 = 46 M2
Mean = 46 ÷ 25 = 1.84 A1
Answer (a): 1.84
(b)
1 – 0.39 = 0.61 B1
Answer (b): 0.61
Question Paper (PDF) • Mark Scheme (PDF)
Question 6 IGCSE Jun 2024 1F Q12
[4 marks]
The table shows information about the number of school lunches each of 30 students had in one week.
Number ofschool lunchesFrequency0215211374451
(a) Work out the mean number of school lunches. [3 marks]
(b) Work out the probability that Alex does **not** take a packed lunch to school. [1 mark]
Worked Solution & Answer
(a)
Total lunches = (0×2) + (1×5) + (2×11) + (3×7) + (4×4) + (5×1) = 0 + 5 + 22 + 21 + 16 + 5 = 69 M2
Mean = 69 ÷ 30 = 2.3 A1
Answer (a): 2.3
(b)
1 − 0.79 = 0.21 B1
Answer (b): 0.21
Question Paper (PDF) • Mark Scheme (PDF)
Question 7 IGCSE Jun 2024 2FR Q15
[4 marks]
The table shows information about the number of oranges in each of 30 bags.
Number of orangesFrequency117128137145151162
(a) Write down the mode of the number of oranges in a bag. [1 mark]
(b) Work out the mean number of oranges in a bag. [3 marks]
Worked Solution & Answer
(a)
Highest frequency is 8, which corresponds to 12 oranges B1
Answer (a): 12
(b)
Total oranges = 11×7 + 12×8 + 13×7 + 14×5 + 15×1 + 16×2 = 77 + 96 + 91 + 70 + 15 + 32 = 381 M2
Mean = 381 ÷ 30 = 12.7 A1
Answer (b): 12.7
Question Paper (PDF) • Mark Scheme (PDF)
Question 8 AQA Nov 2020 3F Q17
[5 marks]
A record was kept of the number of days that 25 students were absent one term.
The chart represents the results.
01234567812345Number of studentsNumber of days absent
(a) Work out the mean number of days absent. [3 marks]
Answer
(b) One of the students is chosen at random.
Work out the probability that the student was absent for less than 4 days. [2 marks]
Answer
Worked Solution & Answer
(a)
Total days = (1 × 5) + (2 × 6) + (3 × 8) + (4 × 2) + (5 × 4) = 5 + 12 + 24 + 8 + 20 = 69 M2
Mean = 69 ÷ 25 = 2.76 days A1
Answer (a): Answer 2.76
(b)
Students absent for 1, 2 or 3 days = 5 + 6 + 8 = 19 M1
Probability = 1925 (or 0.76). A1
Answer (b): Answer 19/25
Question Paper (PDF) • Mark Scheme (PDF)
Question 9 IGCSE Jun 2019 2FR Q12
[5 marks]
Ravina counts the number of matches in each of 40 boxes of matches.
The table shows information about her results.
Number of matchesFrequency2113228238246255
(a) Find the median of the numbers of matches in the boxes. [2 marks]
(b) Work out the mean number of matches. [3 marks]
Worked Solution & Answer
(a)
20th and 21st values both lie in the '22' row (cumulative 13, 21) → median = 22 M1 A1
Answer (a): 22
(b)
(21×13 + 22×8 + 23×8 + 24×6 + 25×5) ÷ 40 = 902 ÷ 40 = 22.55 M2 A1
Answer (b): 22.55
Question Paper (PDF) • Mark Scheme (PDF)
Question 10 IGCSE Jan 2019 1F Q5
[5 marks]
The table shows information about the number of gold medals won by each of 8 countries at the 2016 Olympics.
CountryNumber of gold medalsChina26France10Germany17Great Britain and Northern Ireland27Japan12Russia19South Korea9United States46
(a) Work out the range of the number of gold medals. [1 mark]
(b) Work out the median number of gold medals. [2 marks]
(c) Work out the mean number of gold medals. [2 marks]
Worked Solution & Answer
(a)
(Range: Largest − smallest)
46 − 9 = 37 B1
Answer (a): 37
(b)
Ordered: 9, 10, 12, 17, 19, 26, 27, 46 M1
⇒ (17 + 19)/2 = 18 A1
Answer (b): 18
(c)
166 ÷ 8 = 20.75 M1 A1
Answer (c): 20.75
Question Paper (PDF) • Mark Scheme (PDF)
Score: 0 / 10 (0 / 36 marks)
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Grade 4 Quizzes

24 Topics
4A - Compound interest4B - Indices (index laws)
4C - Prime factors HCF and LCM4D - Real life graphs
4E - Inequalities on a number line4F - Solving inequalities
4G - Forming and solving equations4H - nth term of a linear sequence
4J - Expanding and factorising4K - Pythagoras theorem
4L - Angles in parallel lines4M - Angles in polygons
4N - Surface area4P - Volume of a cuboid
4Q - Volume of a prism4R - Bearings
4S - Cylinders4T - Plans and elevations
4U - Scatter graphs4V - Probability
4W - Averages from tables4X - Reverse mean
4Y - Area of a trapezium4Z - Loci and construction