PAss Functional Skills

Averages and spread

Averages and spread for A Level Engineering OCR Higher: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • OCR
  • Engineering
  • Higher
  • Spec A18 · A9
  • 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.
Work through the method one line at a time and write down what changes at each step.
Worth knowing: ×10\times 10 moves every digit one column left.
5 rows

The averages and spread reference table

Check the answer against an estimate before you move on, so a place-value slip is caught here.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
×10\times 10 moves every digit one column left
Row 2 column 1
Row 2 column 2
≈160\approx 160
Row 3 column 1
Row 3 column 2
×10\times 10 moves every digit one column left

Learning

4 boxes
3 steps

How to work with averages and spread

Read the units in the question before you start; a converted unit is the most common slip.
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.
  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: ×10\times 10 moves every digit one column left
2 rules

Key facts: Averages and spread

The specification wording is precise here, and the mark scheme follows that wording exactly.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.

  • Rule 1

    How averages and spread behaves in the 1st of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 2

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

  • Rule 3

    How averages and spread behaves in the 3rd of the cases the specification names.
    ×10\times 10 moves every digit one column left
5 steps

How to work with averages and spread

Work through the method one line at a time and write down what changes at each step.
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: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: 34×25\frac{3}{4} \times \frac{2}{5}
3 rules

Key facts: Averages and spread

Check the answer against an estimate before you move on, so a place-value slip is caught here.
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: 34×25\frac{3}{4} \times \frac{2}{5}.

  • 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.
    49=7\sqrt{49} = 7

  • Rule 3

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

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Examples

2 boxes
3 marks · worked

Worked example: averages and spread

Work through the method one line at a time and write down what changes at each step.
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.
3 marks · worked

Practice question 8: ×10\times 10 moves every digit one column left

This idea appears again in the higher-mark questions, so it is worth over-learning.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.

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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 A Level Engineering OCR Higher paper?
Yes — it sits in the Data and information strand.