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Averages and spread

Averages and spread for GCSE Food Preparation AQA: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • AQA
  • Food Preparation
  • Spec P4
  • 4 min read
  • 10 revision boxes

Introduction

2 boxes
2 min read

What is averages and spread?

Listen to this box

Transcript

A short spoken summary of averages and spread and where it is used.

A spoken walk-through of averages and spread before you read the notes.
Practise the routine version until it is automatic, then move to the multi-step questions.
2 rows

The averages and spread reference table

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
The layout below is the one the mark scheme expects.

Diagram showing averages and spread laid out step by step

The same idea drawn out, so the method is visible.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
≈160\approx 160
Row 1 column 4
Row 2 column 1
Row 2 column 2
×10\times 10 moves every digit one column left
Row 2 column 4

Learning

6 boxes
3 steps

How to work with averages and spread

This idea appears again in the higher-mark questions, so it is worth over-learning.
  1. Read the question and write down what is being asked for.
  2. Set out the working for averages and spread in the order the method gives.
  3. Substitute the values and simplify.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: ≈160\approx 160
2 rules

Key facts: Averages and spread

The examiner marks the working, so a correct answer with no method still drops marks.

  • Rule 1

    How averages and spread behaves in the 1st of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 2

    How averages and spread behaves in the 2nd of the cases the specification names.
    49=7\sqrt{49} = 7
5 steps

How to work with averages and spread

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.
  1. Read the question and write down what is being asked for.
  2. Set out the working for averages and spread in the order the method gives.
  3. Substitute the values and simplify.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: ×10\times 10 moves every digit one column left.
Answer: x2+5x+6=0x^2 + 5x + 6 = 0
3 rules

Key facts: Averages and spread

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
The layout below is the one the mark scheme expects.

Diagram showing averages and spread laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.

  • Rule 1

    How averages and spread behaves in the 1st of the cases the specification names.
    ≈160\approx 160

  • Rule 2

    How averages and spread behaves in the 2nd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 3

    How averages and spread behaves in the 3rd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2
5 steps

How to work with averages and spread

This idea appears again in the higher-mark questions, so it is worth over-learning.
Worth knowing: ≈160\approx 160.
  1. Read the question and write down what is being asked for.
  2. Set out the working for averages and spread in the order the method gives.
  3. Substitute the values and simplify.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: ≈160\approx 160.
Answer: a2+b2=c2a^2 + b^2 = c^2
2 rules

Key facts: Averages and spread

The examiner marks the working, so a correct answer with no method still drops marks.

  • Rule 1

    How averages and spread behaves in the 1st of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

  • Rule 2

    How averages and spread behaves in the 2nd of the cases the specification names.
    ×10\times 10 moves every digit one column left

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Examples

2 boxes
2 marks · worked

Worked example: averages and spread

Practise the routine version until it is automatic, then move to the multi-step questions.
The layout below is the one the mark scheme expects.

Diagram showing averages and spread laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: 49=7\sqrt{49} = 7.
4 marks · worked

Practice question 10: a2+b2=c2a^2 + b^2 = c^2

The examiner marks the working, so a correct answer with no method still drops marks.

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Common questions

How many marks is averages and spread usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the GCSE Food Preparation AQA paper?
Yes — it sits in the Data and information strand.