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Reverse mean

Free Printable Reverse mean PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 4)

Download free reverse mean worksheets (PDF), GCSE maths past paper questions and worked solutions for Reverse mean (4X). This is a Grade 4 statistics topic from the GCSE questions by topic collection for Foundation and Higher tier crossover GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Maths Made Easy, Dr Austin, 1st Class Maths, Dr Frost (B. Blocks), E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our reverse mean revision notes and worked examples with diagrams, try real GCSE past paper reverse mean questions with step-by-step solutions, or download a PDF of all reverse mean worksheet links.

Free Reverse mean PDF Worksheets & Answers

Grade 4 • Topic 4X
Resource Questions Answers
GCSE past paper questions & solutions
 Qs Ans
Question booklet & answer sheet
 Qs Ans
MME worksheet & model answers
 Qs Ans
Practice grid / worksheet & answers
 Qs Ans
Edexcel exam questions & solutions
 Qs Ans
AQA exam questions & solutions
 Qs Ans
Building Blocks skill sheet & answers
 Qs Ans
GCSE topic booklet & answers
 Qs Ans
PMT (Edxl)
Edexcel GCSE topic questions & solutions
 Qs Ans
PMT (AQA)
AQA GCSE topic questions & solutions
 Qs Ans
PMT (IGCSE)
Edexcel IGCSE topic questions & solutions
 Qs Ans
Self-marking online worksheet
 Page
Grade 4 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
GCSE Maths Grade 4 Revision Notes & Method

Guide to Reverse mean: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

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
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Reverse mean Questions & Answers

Past Paper Example 1 IGCSE Jan 2022 2FR Q25 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
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.
Worked Solution & Mark Scheme (3 marks)
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
Past Paper Example 2 AQA Jun 2022 3F Q14 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
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]
(b) Work out the mean number of games played.
Give your answer as a decimal. [3 marks]
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
Students who played 3, 4, or 5 games: 4 + 1 + 3 = 8. B1
Answer (a): Answer 8
Part (b) Solution:
(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
Past Paper Example 3 AQA Nov 2020 3F Q17 5 marks
Full Paper (PDF) • Mark Scheme (PDF)
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]
(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]
Worked Solution & Mark Scheme (5 marks)
Part (a) Solution:
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
Part (b) Solution:
Students absent for 1, 2 or 3 days = 5 + 6 + 8 = 19 M1
Probability = 1925 (or 0.76). A1
Answer (b): Answer 19/25

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