Where can I download free averages PDF worksheets with answers?

On this MathsLinks page you can download free printable averages PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, Maths Genie, Maths4Everyone, Corbett Practice, Corbett Textbook, plus a printable one-page averages revision guide.

What GCSE grade is averages (2T)?

Averages (topic code 2T) is a Grade 2 statistics topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Averages Worksheets (PDF) with Answers — GCSE Maths

Free Averages PDF Worksheets & Answers

Grade 2 • Topic 2T

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Maths4Everyone GCSE 9–1 practice booklet & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Maths Made Easy MME worksheet & model answers	Qs	Ans
Dr Frost GCSE worksheet & solutions	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
1st Class Maths (Edxl) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (AQA) AQA exam questions & solutions	Qs	Ans
E Classroom 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
The Maths Room Online topic notes & examples	Page
Cognito Interactive online lesson & practice	Page
esheets Self-marking online worksheet	Page

Grade 2 topics
2A - Calculation problems	2B - Using a calculator
2C - Systematic listing	2D - Fraction of an amount
2E - FDP	2F - Simplifying algebra
2G - Writing an expression	2H - Function machines
2J - Solving one step equations	2K - Angles
2L - Area and perimeter	2M - Reading scales
2N - Probability & Probability Scale	2P - Frequency polygons
2Q - Unitary method	2R - Bar charts
2S - Pie charts	2T - Averages
2U - Stem and leaf diagrams

Explanation:

Memorise the four summary statistics: Mode = most common value; Median = middle value after putting the list in order from smallest to largest; Mean = Total of values ÷ Number of values; and Range = Biggest − Smallest (range measures spread, not average).

If there is an even number of values, there are two numbers in the middle — add those two middle numbers together and divide by 2 to find the median.

Example 1: Find the mode, median, mean, and range of:
8, 3, 5, 9, 3, 10, 4

Solution:

Order first: 3, 3, 4, 5, 8, 9, 10 (7 values)

• Mode: 3 (appears twice) • Median: 5 (4th value)

• Mean: 42 ÷ 7 = 6

• Range: 10 − 3 = 7

Example 2: Find the median, mean, and range of:
12, 7, 15, 9, 18, 11

Solution:

Order first: 7, 9, 11, 12, 15, 18 (6 values)

• Median: Halfway between 11 & 12 = 11 + 122 = 11.5

• Mean: 72 ÷ 6 = 12

• Range: 18 − 7 = 11

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Averages Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 Eduqas Nov 2024 2F Q11 6 marks

Full Paper (PDF) • Mark Scheme (PDF)

Jeff and Ava have a pack of numbered cards.

(a) Jeff selects three cards: 3, 11, 6. [2 marks]

Jeff selects a fourth card.
The median of the numbers on his four cards is 7.5.
What number is on the fourth card?

(b) Ava selects three cards from the pack.
The mean of the numbers on these three cards is 8.
Ava selects a fourth card.
The mean of the numbers on her four cards is 9.5.
What number is on the fourth card? [4 marks]

Worked Solution & Mark Scheme (6 marks)

Part (a) Solution:

Ordered given cards: 3, 6, 11 M1
For 4 cards with median 7.5, the sum of the two middle cards must be 7.5 × 2 = 15
Middle cards are 6 and the fourth card: 6 + x = 15 ⇒ x = 9
Ordered: 3, 6, 9, 11
median = (6 + 9)/2 = 7.5. A1

Answer (a): 9

Part (b) Solution:

Total of 3 cards = 3 × 8 = 24 M2
Total of 4 cards = 4 × 9.5 = 38 M1
Fourth card = 38 - 24 = 14. A1

Answer (b): 14

Past Paper Example 2 AQA Nov 2017 2F Q18 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

Here are five cards:
[1] [5] [7] [9] [11]

One of the cards is removed.
The mean of the numbers on the remaining four cards is 6
Which card was removed?
You must show your working.

Worked Solution & Mark Scheme (3 marks)

Sum of all five cards = 1 + 5 + 7 + 9 + 11 = 33 M1
Sum of remaining four cards = 4 × 6 = 24 M1
Removed card = 33 - 24 = 9 A1

Answer: Answer 9

Past Paper Example 3 Eduqas Nov 2017 1F Q7 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

(a) There are 4 rowers in a boat.
The mode and median of their shoe sizes are both 11.
The range of their shoe sizes is 4.
One of the rowers has size 13 shoes.
What is the shoe size of each rower?
(b) (i) How many teams does the rowing club have in total?
(b) (ii) Rona is a junior rower at the club.
What is the probability that Rona rows in a junior 8-seater boat?

(b) How many teams does the rowing club have in total? [1 mark]

Rona is a junior rower at the club.
What is the probability that Rona rows in a junior 8-seater boat? [1 mark]

Worked Solution & Mark Scheme (4 marks)

Part (a) Solution:

Since one rower is 13 and the range is 4, the smallest size is 13 - 4 = 9 M1
With 4 rowers, the median is the average of the 2nd and 3rd sizes: (b + c) / 2 = 11
Since the mode is 11, the two middle values must both be 11
Hence the sizes in order are 9, 11, 11, 13. A1

Answer (a): 9, 11, 11, 13

Part (b) Solution:

2-seater: 3 + 2 + 1 = 6
4-seater: 5 + 1 + 3 = 9
8-seater: 2 + 1 + 0 = 3
Total = 6 + 9 + 3 = 18 B1

Answer (b): 18

Part Solution:

The bar chart shows there are 0 junior 8-seater boat teams, so the probability is 0 (or 0%). B1

Answer : 0

← 2S Pie charts

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Averages

Free Averages PDF Worksheets & Answers

Guide to Averages: Explanation, Diagrams & Worked Examples

GCSE Past Paper Averages Questions & Answers