📊 Statistics District · Reasoning

Outliers

Use real data and precise language to work confidently with outliers. In this lesson, focus on data work begins with a clear question and ends with a supported conclusion.

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Understand Outliers

Use real data and precise language to work confidently with outliers. In this lesson, focus on data work begins with a clear question and ends with a supported conclusion.

Data work begins with a clear question and ends with a supported conclusion. Choose an honest representation, calculate relevant summaries and quote evidence rather than relying on vague impressions. For outliers, the final written answer should make that exact relationship visible rather than hiding it inside an unexplained result.

Start here

Outliers: Data work begins with a clear question and ends with a supported conclusion. Trace every quoted value back to the table or chart and ask whether the conclusion answers the original question. Keep the outliers representation visible until the final line.

Picture the idea

Build a frequency table from raw values and switch between chart and summary views before writing a conclusion. Use the model to explain one change you notice while working on outliers.

Check as you go

Trace every quoted value back to the table or chart and ask whether the conclusion answers the original question. Write that check beside the final outliers answer.

Key vocabulary

datafrequencysamplecomparisonevidenceoutliers

Rules and key facts

Given information: Outliers — Identify the outlier in 4, 5, 5, 6, 7, 30. Method choice: Identify the mathematical relationship shown by the given values. Show one clear calculation and check it against the information in the question. Calculation or reasoning: Use the given values with the stated relationship. Show the calculation clearly to obtain 30. Final answer: 30. Check: Show one clear calculation and check it against the information in the question.

  • Identify the question and the type of data.
  • Organise values carefully and choose a suitable display or summary.
  • Calculate or read the relevant evidence.
  • Write a contextual conclusion supported by values. Record the check explicitly for outliers.

Step-by-step method

  1. Identify the question and the type of data.
  2. Organise values carefully and choose a suitable display or summary.
  3. Calculate or read the relevant evidence.
  4. Write a contextual conclusion supported by values. Record the check explicitly for outliers.

What you need first

  • Recognise the vocabulary: data, frequency, sample.
  • Be able to explain the purpose of outliers before calculating.
  • Keep the relevant values, units and representation visible while you work.

Real-world use

  • Survey design
  • Evidence-based decisions

Visual / interactive

See the idea, then move it around

Skip to Practice

Build a frequency table from raw values and switch between chart and summary views before writing a conclusion. Use the model to explain one change you notice while working on outliers.

Interactive maths model Connected to this topic; move controls, check outputs, then earn XP only from verified actions.
Responsive · validated · topic linked

Worked examples

Examples, methods and exam thinking

Level 1 · Foundation

Understand the idea with small numbers, one representation and one clear step.

Level 2 · Secure

Use the standard Year 8 method with mixed examples and normal wording.

Level 3 · Challenge

Handle multi-step or less familiar questions and explain choices.

Level 4 · Exam-style

Solve a worded question, show reasoning, check accuracy and write a final sentence.

Foundation example

Build confidence

Given information: Outliers — Identify the outlier in 4, 5, 5, 6, 7, 30. Method choice: use the outliers method and show each step with the stated values. Calculation or reasoning: Identify the outlier in 4, 5, 5, 6, 7, 30. Final answer: 30. Check: substitute or compare with the original information to confirm the result fits the question.

  1. Identify the question and the type of data.
  2. Organise values carefully and choose a suitable display or summary.
  3. Calculate or read the relevant evidence.
Secure example

Use the normal method

Given information: Outliers — Identify the outlier in 4, 5, 5, 6, 7, 47. Method choice: use the outliers method and show each step with the stated values. Calculation or reasoning: Identify the outlier in 4, 5, 5, 6, 7, 47. Final answer: 47. Check: substitute or compare with the original information to confirm the result fits the question.

Check: Check the outliers result against the original information.

Challenge example

Stretch the idea

Given information: Outliers — Identify the outlier in 4, 5, 5, 6, 7, 64. Method choice: use the outliers method and show each step with the stated values. Calculation or reasoning: Identify the outlier in 4, 5, 5, 6, 7, 64. Final answer: 64. Check: substitute or compare with the original information to confirm the result fits the question.

Try explaining why each step works before checking the answer.

Exam-style example

Show your reasoning

Given information: Outliers — Identify the outlier in 4, 5, 5, 6, 7, 81. Method choice: use the outliers method and show each step with the stated values. Calculation or reasoning: Identify the outlier in 4, 5, 5, 6, 7, 81. Final answer: 81. Check: substitute or compare with the original information to confirm the result fits the question.

Exam tip: Underline the units and command word. Show the key calculation and write the answer in context.

Common mistakes

  • Using a vague conclusion without numbers. This is a key trap when answering outliers questions.
  • Choosing a display that hides an important feature.

How to check your answer

Trace every quoted value back to the table or chart and ask whether the conclusion answers the original question. Write that check beside the final outliers answer.

Extension challenge

Create a outliers problem with a tempting incorrect answer. Solve it, apply the check, and explain exactly where the incorrect method breaks down.

Practice · always open

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Games · always open

Outliers challenge

Use evidence case controls to solve three checked outliers rounds. Solve at least two of three marked rounds and use feedback to correct any error.

Press Start Game to enter a topic-specific maths arena.

Boss challenge

Challenge Outliers Guardian

The boss is available when you feel ready. Boss victory badges and legendary status still require a strong pass.

Outliers Guardian

Timed mixed-difficulty battle. Practice first if you want, or jump in and learn from feedback.

12 mixed questions5:00 timer×2 XP multiplier
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Study cards and flashcards · always open

Study the essentials quickly

Study cards

Core idea

Outliers: Data work begins with a clear question and ends with a supported conclusion. Trace every quoted value back to the table or chart and ask whether the conclusion answers the original question. Keep the outliers representation visible until the final line.

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Key vocabulary

data · frequency · sample · comparison · evidence · outliers

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Rules

Identify the question and the type of data. Organise values carefully and choose a suitable display or summary. Calculate or read the relevant evidence. Write a contextual conclusion supported by values. Record the check explicitly for outliers.

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Formula / fact

Given information: Outliers — Identify the outlier in 4, 5, 5, 6, 7, 30. Method choice: Identify the mathematical relationship shown by the given values. Show one clear calculation and check it against the information in the question. Calculation or reasoning: Use the given values with the stated relationship. Show the calculation clearly to obtain 30. Final answer: 30. Check: Show one clear calculation and check it against the information in the question.

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Foundation example

Given information: Outliers — Identify the outlier in 4, 5, 5, 6, 7, 30. Method choice: use the outliers method and show each step with the stated values. Calculation or reasoning: Identify the outlier in 4, 5, 5, 6, 7, 30. Final answer: 30. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Secure example

Given information: Outliers — Identify the outlier in 4, 5, 5, 6, 7, 47. Method choice: use the outliers method and show each step with the stated values. Calculation or reasoning: Identify the outlier in 4, 5, 5, 6, 7, 47. Final answer: 47. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Challenge example

Given information: Outliers — Identify the outlier in 4, 5, 5, 6, 7, 64. Method choice: use the outliers method and show each step with the stated values. Calculation or reasoning: Identify the outlier in 4, 5, 5, 6, 7, 64. Final answer: 64. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Exam-style example

Given information: Outliers — Identify the outlier in 4, 5, 5, 6, 7, 81. Method choice: use the outliers method and show each step with the stated values. Calculation or reasoning: Identify the outlier in 4, 5, 5, 6, 7, 81. Final answer: 81. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Common mistake

Using a vague conclusion without numbers. This is a key trap when answering outliers questions.

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Exam tip

For outliers, show the key representation before the final calculation. Use this final check: Trace every quoted value back to the table or chart and ask whether the conclusion answers the original question.

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Real-world use

Survey design, Evidence-based decisions

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Checklist

I can explain outliers, use the method, check for mistakes, and answer an exam-style question.

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Flashcards

I’m Stuck

Help for Outliers

Use this whenever a question feels confusing. Nothing here is locked.

Simple explanation

Outliers: Data work begins with a clear question and ends with a supported conclusion. Trace every quoted value back to the table or chart and ask whether the conclusion answers the original question. Keep the outliers representation visible until the final line.

Think of outliers as a careful model: make the important values visible, change one thing at a time, and use the check to prove the answer fits.

Step-by-step breakdown

  1. Identify the question and the type of data.
  2. Organise values carefully and choose a suitable display or summary.
  3. Calculate or read the relevant evidence.
  4. Write a contextual conclusion supported by values. Record the check explicitly for outliers.

Hint 1

Start by naming the given information and the exact result required for outliers.

Hint 2

Identify the question and the type of data.

Full worked solution

Given information: Outliers — Identify the outlier in 4, 5, 5, 6, 7, 30. Method choice: use the outliers method and show each step with the stated values. Calculation or reasoning: Identify the outlier in 4, 5, 5, 6, 7, 30. Final answer: 30. Check: substitute or compare with the original information to confirm the result fits the question.

Method: Identify the question and the type of data. → Organise values carefully and choose a suitable display or summary. → Calculate or read the relevant evidence. → Write a contextual conclusion supported by values. Record the check explicitly for outliers.

Common mistake warning

Using a vague conclusion without numbers. This is a key trap when answering outliers questions.

Choose a support button above when you need a nudge.

Mastery milestones

Badges reward learning, not locked clicking

  • I can explain outliers in my own words.
  • I can use these words accurately: data, frequency, sample.
  • I can follow the 4-step method without guessing.
  • I can avoid this mistake: Using a vague conclusion without numbers.
  • I can apply this check: Trace every quoted value back to the table or chart and ask whether the conclusion answers the original question.
🥉 Bronze Badge Foundation completed
🥈 Silver Badge Guide completed
🥇 Gold Badge Practice completed
💎 Platinum Badge Mastery passed
🐉 Legendary Badge Boss defeated