📊 Statistics District · Averages

Median

Calculate and interpret the median as a useful summary of a real data set. In this lesson, focus on the median is the middle value after the data is ordered.

← Back to Region Back to Dashboard
🏅
Median Pathfinder Earned through mastery, boss success and strong scores — not by clicking through locks.

Player progress

Level 1 · Apprentice

0 / 100 XP

0 day streak 0% topic learning 0 completed topics 0 badges 0 boss wins 10 open sections4 practice levels

Learn · open now

Understand Median

Calculate and interpret the median as a useful summary of a real data set. In this lesson, focus on the median is the middle value after the data is ordered.

The median is the middle value after the data is ordered. It depends on position rather than the total, which makes it less sensitive than the mean to a very large outlier. For median, the final written answer should make that exact relationship visible rather than hiding it inside an unexplained result.

Start here

Median: The median is the middle value after the data is ordered. Count values on each side of the proposed median; the ordered list should balance around the centre. Keep the median representation visible until the final line.

Picture the idea

Drag values into order and highlight the central position or central pair. Use the model to explain one change you notice while working on median.

Check as you go

Count values on each side of the proposed median; the ordered list should balance around the centre. Write that check beside the final median answer.

Key vocabulary

medianordered datamiddle positioneven numberfrequency

Rules and key facts

Given information: Median — Find the median of the unordered list 4, 3, 10, 2, 2. Method choice: Put the values in order before finding the middle. For an even number of values, find the mean of the middle pair. Calculation or reasoning: Order the values: 2, 2, 3, 4, 10. The middle value is 3. Final answer: 3. Check: For an even number of values, find the mean of the middle pair.

  • Order the data from smallest to largest.
  • Locate the middle position.
  • If there are two middle values, find their mean.
  • Check the ordered list before writing the median.

Step-by-step method

  1. Order the data from smallest to largest.
  2. Locate the middle position.
  3. If there are two middle values, find their mean.
  4. Check the ordered list before writing the median.

What you need first

  • Recognise the vocabulary: median, ordered data, middle position.
  • Be able to explain the purpose of median before calculating.
  • Keep the relevant values, units and representation visible while you work.

Real-world use

  • House-price summaries
  • Typical waiting times

Visual / interactive

See the idea, then move it around

Skip to Practice

Drag values into order and highlight the central position or central pair. Use the model to explain one change you notice while working on median.

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: Median — Find the median of the unordered list 4, 3, 10, 2, 2. Method choice: use the median method and show each step with the stated values. Calculation or reasoning: Order the values: 2, 2, 3, 4, 10. The middle value is 3. Final answer: 3. Check: substitute or compare with the original information to confirm the result fits the question.

  1. Order the data from smallest to largest.
  2. Locate the middle position.
  3. If there are two middle values, find their mean.
Secure example

Use the normal method

Given information: Median — A frequency table has values 3, 3, 14, 14 with frequencies 1, 2, 3, 1. Find the median. Method choice: use the median method and show each step with the stated values. Calculation or reasoning: There are 7 values in total. The 4th value in order is 14, so the median is 14. Final answer: 14. Check: substitute or compare with the original information to confirm the result fits the question.

Check: Check the median result against the original information.

Challenge example

Stretch the idea

Given information: Median — The list 3, 13, 9, 7, 80 contains an outlier. Which average is usually less affected by the outlier: mean or median? Method choice: use the median method and show each step with the stated values. Calculation or reasoning: The extreme value 80 pulls the mean more strongly. The median depends on the middle position, so median is less affected. Final answer: median. 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: Median — Find the median of this even list: 3, 12, 4, 4, 12, 22. Method choice: use the median method and show each step with the stated values. Calculation or reasoning: Order the six values: 3, 4, 4, 12, 12, 22. Average the middle pair: (4 + 12) ÷ 2 = 8. Final answer: 8. 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

  • Finding the middle before ordering. This is a key trap when answering median questions.
  • Choosing both middle values without averaging when the count is even.

How to check your answer

Count values on each side of the proposed median; the ordered list should balance around the centre. Write that check beside the final median answer.

Extension challenge

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

Practice · always open

Question practice with hints and full solutions

Choose a difficulty, answer questions, ask for hints, see the method, retry, or generate a similar question. XP rewards accurate work and improved scores.

I’m Stuck

Year 8 practice studio

Practice Studio

Foundation, secure, challenge and exam-style questions are available immediately with instant feedback.

Progress 0/0 Score 0 Streak 0
I’m Stuck

Answer the questions, then check your score.

Score tracking: Answer questions to start tracking your score.

Games · always open

Median challenge

Use median sort controls to solve three checked median 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 Median Guardian

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

Median 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
Timer readyAwaiting battle

Study cards and flashcards · always open

Study the essentials quickly

Study cards

Core idea

Median: The median is the middle value after the data is ordered. Count values on each side of the proposed median; the ordered list should balance around the centre. Keep the median representation visible until the final line.

Tap to mark reviewed
Key vocabulary

median · ordered data · middle position · even number · frequency

Tap to mark reviewed
Rules

Order the data from smallest to largest. Locate the middle position. If there are two middle values, find their mean. Check the ordered list before writing the median.

Tap to mark reviewed
Formula / fact

Given information: Median — Find the median of the unordered list 4, 3, 10, 2, 2. Method choice: Put the values in order before finding the middle. For an even number of values, find the mean of the middle pair. Calculation or reasoning: Order the values: 2, 2, 3, 4, 10. The middle value is 3. Final answer: 3. Check: For an even number of values, find the mean of the middle pair.

Tap to mark reviewed
Foundation example

Given information: Median — Find the median of the unordered list 4, 3, 10, 2, 2. Method choice: use the median method and show each step with the stated values. Calculation or reasoning: Order the values: 2, 2, 3, 4, 10. The middle value is 3. 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: Median — A frequency table has values 3, 3, 14, 14 with frequencies 1, 2, 3, 1. Find the median. Method choice: use the median method and show each step with the stated values. Calculation or reasoning: There are 7 values in total. The 4th value in order is 14, so the median is 14. Final answer: 14. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Challenge example

Given information: Median — The list 3, 13, 9, 7, 80 contains an outlier. Which average is usually less affected by the outlier: mean or median? Method choice: use the median method and show each step with the stated values. Calculation or reasoning: The extreme value 80 pulls the mean more strongly. The median depends on the middle position, so median is less affected. Final answer: median. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Exam-style example

Given information: Median — Find the median of this even list: 3, 12, 4, 4, 12, 22. Method choice: use the median method and show each step with the stated values. Calculation or reasoning: Order the six values: 3, 4, 4, 12, 12, 22. Average the middle pair: (4 + 12) ÷ 2 = 8. Final answer: 8. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Common mistake

Finding the middle before ordering. This is a key trap when answering median questions.

Tap to mark reviewed
Exam tip

For median, show the key representation before the final calculation. Use this final check: Count values on each side of the proposed median; the ordered list should balance around the centre.

Tap to mark reviewed
Real-world use

House-price summaries, Typical waiting times

Tap to mark reviewed
Checklist

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

Tap to mark reviewed

Flashcards

I’m Stuck

Help for Median

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

Simple explanation

Median: The median is the middle value after the data is ordered. Count values on each side of the proposed median; the ordered list should balance around the centre. Keep the median representation visible until the final line.

Think of median 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. Order the data from smallest to largest.
  2. Locate the middle position.
  3. If there are two middle values, find their mean.
  4. Check the ordered list before writing the median.

Hint 1

Order the data first.

Hint 2

For an even number of values, average the middle pair.

Full worked solution

Given information: Median — Find the median of the unordered list 4, 3, 10, 2, 2. Method choice: use the median method and show each step with the stated values. Calculation or reasoning: Order the values: 2, 2, 3, 4, 10. The middle value is 3. Final answer: 3. Check: substitute or compare with the original information to confirm the result fits the question.

Method: Order the data from smallest to largest. → Locate the middle position. → If there are two middle values, find their mean. → Check the ordered list before writing the median.

Common mistake warning

Finding the middle before ordering. This is a key trap when answering median questions.

Choose a support button above when you need a nudge.

Mastery milestones

Badges reward learning, not locked clicking

  • I can explain median in my own words.
  • I can use these words accurately: median, ordered data, middle position.
  • I can follow the 4-step method without guessing.
  • I can avoid this mistake: Finding the middle before ordering.
  • I can apply this check: Count values on each side of the proposed median; the ordered list should balance around the centre.
🥉 Bronze Badge Foundation completed
🥈 Silver Badge Guide completed
🥇 Gold Badge Practice completed
💎 Platinum Badge Mastery passed
🐉 Legendary Badge Boss defeated