PAss Functional Skills

Averages and spread

Averages and spread for GCSE History AQA: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • AQA
  • History
  • Spec G7 · G4 · G18
  • 14 min read
  • 8 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.
The examiner marks the working, so a correct answer with no method still drops marks.
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: ×10\times 10 moves every digit one column left.
6 rows

The averages and spread reference table

This idea appears again in the higher-mark questions, so it is worth over-learning.
Term
Meaning
Example
Common slip
Marks
Row 1 column 1
Row 1 column 2
≈160\approx 160
Row 1 column 4
Row 1 column 5
Row 2 column 1
Row 2 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 2 column 4
Row 2 column 5
Row 3 column 1
Row 3 column 2
×10\times 10 moves every digit one column left
Row 3 column 4
Row 3 column 5

Learning

4 boxes
5 steps

How to work with averages and spread

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
Worth knowing: ×10\times 10 moves every digit one column left.
  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.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: ≈160\approx 160.
Answer: ≈160\approx 160
2 rules

Key facts: Averages and spread

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: ≈160\approx 160.

  • Rule 1

    How averages and spread behaves in the 1st of the cases the specification names.
    ×10\times 10 moves every digit one column left

  • 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

  • Rule 3

    How averages and spread behaves in the 3rd of the cases the specification names.
    49=7\sqrt{49} = 7
4 steps

How to work with averages and spread

The examiner marks the working, so a correct answer with no method still drops marks.
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.
  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: x2+5x+6=0x^2 + 5x + 6 = 0
3 rules

Key facts: Averages and spread

This idea appears again in the higher-mark questions, so it is worth over-learning.

  • 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.
    ≈160\approx 160

  • Rule 3

    How averages and spread behaves in the 3rd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

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Examples

2 boxes
3 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: ×10\times 10 moves every digit one column left.
4 marks · worked

Practice question 8: 49=7\sqrt{49} = 7

Practise the routine version until it is automatic, then move to the multi-step questions.

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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 History AQA paper?
Yes — it sits in the Data and information strand.