📊 Statistics District · Averages

Mode

Calculate and interpret the mode as a useful summary of a real data set. In this lesson, focus on the mode identifies the value or category with the greatest frequency.

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Understand Mode

Calculate and interpret the mode as a useful summary of a real data set. In this lesson, focus on the mode identifies the value or category with the greatest frequency.

The mode identifies the value or category with the greatest frequency. A data set can have no mode or more than one mode; grouped data reports a modal class rather than an exact value. For mode, the final written answer should make that exact relationship visible rather than hiding it inside an unexplained result.

Start here

Mode: The mode identifies the value or category with the greatest frequency. Count occurrences again and confirm no other value has a greater or equal frequency. Keep the mode representation visible until the final line.

Picture the idea

Stack identical values or class frequencies so the tallest stack reveals the mode. Use the model to explain one change you notice while working on mode.

Check as you go

Count occurrences again and confirm no other value has a greater or equal frequency. Write that check beside the final mode answer.

Key vocabulary

modefrequencymost commonmodal classcategory

Rules and key facts

Given information: Mode — Find the mode of 3, 2, 3, 4, 3, 2. Method choice: Look for the value or class that occurs most often. Use frequency, not size, when deciding which value is the mode. Calculation or reasoning: 3 occurs three times, more than any other value. Final answer: 3. Check: Use frequency, not size, when deciding which value is the mode.

  • Record each value or class frequency.
  • Compare the frequencies.
  • Identify the greatest frequency.
  • State the matching value, category or modal class precisely. Record the check explicitly for mode.

Step-by-step method

  1. Record each value or class frequency.
  2. Compare the frequencies.
  3. Identify the greatest frequency.
  4. State the matching value, category or modal class precisely. Record the check explicitly for mode.

What you need first

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

Real-world use

  • Popular choices
  • Stock planning

Visual / interactive

See the idea, then move it around

Skip to Practice

Stack identical values or class frequencies so the tallest stack reveals the mode. Use the model to explain one change you notice while working on mode.

Mean / median / mode / range calculator 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: Mode — Find the mode of 3, 2, 3, 4, 3, 2. Method choice: use the mode method and show each step with the stated values. Calculation or reasoning: 3 occurs three times, more than any other value. Final answer: 3. Check: substitute or compare with the original information to confirm the result fits the question.

  1. Record each value or class frequency.
  2. Compare the frequencies.
  3. Identify the greatest frequency.
Secure example

Use the normal method

Given information: Mode — Find the mode of 3, 14, 3, 14, 3, 14. Method choice: use the mode method and show each step with the stated values. Calculation or reasoning: 3 occurs three times, more than any other value. Final answer: 3. Check: substitute or compare with the original information to confirm the result fits the question.

Check: Check the mode result against the original information.

Challenge example

Stretch the idea

Given information: Mode — Find the mode of 3, 13, 3, 9, 3, 13. Method choice: use the mode method and show each step with the stated values. Calculation or reasoning: 3 occurs three times, more than any other value. Final answer: 3. 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: Mode — Find the mode of 3, 12, 3, 4, 3, 12. Method choice: use the mode method and show each step with the stated values. Calculation or reasoning: 3 occurs three times, more than any other value. Final answer: 3. 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

  • Choosing the largest value rather than the most frequent. This is a key trap when answering mode questions.
  • Inventing an exact mode from grouped data.

How to check your answer

Count occurrences again and confirm no other value has a greater or equal frequency. Write that check beside the final mode answer.

Extension challenge

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

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Mode challenge

Use mode stack controls to solve three checked mode 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

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Study cards

Core idea

Mode: The mode identifies the value or category with the greatest frequency. Count occurrences again and confirm no other value has a greater or equal frequency. Keep the mode representation visible until the final line.

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Key vocabulary

mode · frequency · most common · modal class · category

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Rules

Record each value or class frequency. Compare the frequencies. Identify the greatest frequency. State the matching value, category or modal class precisely. Record the check explicitly for mode.

Tap to mark reviewed
Formula / fact

Given information: Mode — Find the mode of 3, 2, 3, 4, 3, 2. Method choice: Look for the value or class that occurs most often. Use frequency, not size, when deciding which value is the mode. Calculation or reasoning: 3 occurs three times, more than any other value. Final answer: 3. Check: Use frequency, not size, when deciding which value is the mode.

Tap to mark reviewed
Foundation example

Given information: Mode — Find the mode of 3, 2, 3, 4, 3, 2. Method choice: use the mode method and show each step with the stated values. Calculation or reasoning: 3 occurs three times, more than any other value. Final answer: 3. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Secure example

Given information: Mode — Find the mode of 3, 14, 3, 14, 3, 14. Method choice: use the mode method and show each step with the stated values. Calculation or reasoning: 3 occurs three times, more than any other value. Final answer: 3. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Challenge example

Given information: Mode — Find the mode of 3, 13, 3, 9, 3, 13. Method choice: use the mode method and show each step with the stated values. Calculation or reasoning: 3 occurs three times, more than any other value. Final answer: 3. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Exam-style example

Given information: Mode — Find the mode of 3, 12, 3, 4, 3, 12. Method choice: use the mode method and show each step with the stated values. Calculation or reasoning: 3 occurs three times, more than any other value. Final answer: 3. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Common mistake

Choosing the largest value rather than the most frequent. This is a key trap when answering mode questions.

Tap to mark reviewed
Exam tip

For mode, show the key representation before the final calculation. Use this final check: Count occurrences again and confirm no other value has a greater or equal frequency.

Tap to mark reviewed
Real-world use

Popular choices, Stock planning

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Checklist

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

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Flashcards

I’m Stuck

Help for Mode

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

Simple explanation

Mode: The mode identifies the value or category with the greatest frequency. Count occurrences again and confirm no other value has a greater or equal frequency. Keep the mode representation visible until the final line.

Think of mode 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. Record each value or class frequency.
  2. Compare the frequencies.
  3. Identify the greatest frequency.
  4. State the matching value, category or modal class precisely. Record the check explicitly for mode.

Hint 1

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

Hint 2

Record each value or class frequency.

Full worked solution

Given information: Mode — Find the mode of 3, 2, 3, 4, 3, 2. Method choice: use the mode method and show each step with the stated values. Calculation or reasoning: 3 occurs three times, more than any other value. Final answer: 3. Check: substitute or compare with the original information to confirm the result fits the question.

Method: Record each value or class frequency. → Compare the frequencies. → Identify the greatest frequency. → State the matching value, category or modal class precisely. Record the check explicitly for mode.

Common mistake warning

Choosing the largest value rather than the most frequent. This is a key trap when answering mode questions.

Choose a support button above when you need a nudge.

Mastery milestones

Badges reward learning, not locked clicking

  • I can explain mode in my own words.
  • I can use these words accurately: mode, frequency, most common.
  • I can follow the 4-step method without guessing.
  • I can avoid this mistake: Choosing the largest value rather than the most frequent.
  • I can apply this check: Count occurrences again and confirm no other value has a greater or equal frequency.
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