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histograms & box plots

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4 detailed 50-minute lessons with teaching scripts, worked examples, parent guides, and assessment criteria.

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Lesson Overview

Total Lessons: 4
Tier: Foundation and Higher
Duration: 50 minutes per lesson (200 minutes total)
Exam Boards: AQA, Edexcel, OCR, Eduqas, CCEA

Learning Objectives

Prerequisites

Materials & Equipment

Lesson 1: Introduction: histograms & box plots

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Write down everything you already know about histograms & box plots. Then check against the key terms: key terms from histograms & box plots. Use a mini-whiteboard or paper.

Main Content (35 minutes)

Parent/Teacher Guide:
Before lesson: Read the script below. Pre-teach key vocab: key terms from histograms & box plots.
If stuck: Re-read the revision notes (link above), then break the content into smaller steps.
Extension: See the Stretch & Challenge ideas in Lesson 4.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: histograms & box plots. By the end you will be able to answer exam questions on it unaided. It connects to the rest of Statistics because the ideas here recur across the spec."
Mins 5-20 - Direct Instruction: Work through the core ideas below one at a time; after each, ask your student to explain it back in their own words.
Mins 20-30 - Guided Practice: Model the worked example together, then let your student attempt the first practice question with guidance.
Mins 30-35 - Independent Practice: 2-3 practice questions from Lesson 3 below, with immediate feedback.
First Look

Start with the revision notes summary, then attempt: explain the key ideas of histograms & box plots

Plenary (5 minutes)

Check Out

Your student states one thing they learned and one question they still have about histograms & box plots.

Lesson 2: Core Concepts: histograms & box plots

Duration: 50 minutes

Starter Activity (5 minutes)

Review Previous Lesson

Quick recap: write 3 key points from Lesson 1 on histograms & box plots. Check them against the notes below.

Main Content (35 minutes)

Key Fact: A histogram displays continuous data using bars with no gaps between them; the area of each bar (not the height) is proportional to the frequency.
Key Fact: Frequency density = frequency ÷ class width; the vertical axis of a histogram shows frequency density, not frequency.
Key Fact: When class widths are equal, the bar heights are proportional to the frequencies and frequency density is simply frequency ÷ class width.
Key Fact: When class widths are unequal, you must calculate frequency density for each bar; the height no longer equals the frequency.
Key Fact: The total area of all bars in a histogram equals the total frequency; you can find missing frequencies by setting up area equations.
Key Fact: A box plot (box-and-whisker diagram) shows five key values: minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum.

Practice (10 minutes)

Q: explain the key ideas of histograms & box plots

Answer:

Plenary (5 minutes)

Explain Back

Your student teaches the key points back to you without looking. Fill any gaps immediately.

Lesson 3: Application: histograms & box plots

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Recall the key terms: key terms from histograms & box plots. Define each in one sentence.

Main Content (35 minutes)

Parent/Teacher Guide: Let your student attempt each question alone first, then compare with the model answer. Award method marks for correct working even if the final answer is wrong.

Work through the practice questions on the revision notes page for this topic.

Plenary (5 minutes)

Error Review

Review any questions answered incorrectly. Identify whether the error was knowledge, method, or reading the question.

Lesson 4: Exam Practice: histograms & box plots

Duration: 50 minutes

Starter Activity (5 minutes)

Command Words

Review what these command words require: state (one point), describe (say what happens), explain (say why), compare (both sides), evaluate (judgement).

Main Content (35 minutes)

Extended Answer

Extended question: Full-Mark Response The frequency table shows the times taken for 120 runners to complete a race. Draw a histogram. 0–10 min: frequency 15, 10–20 min: frequency 40, 20–40 min: frequency 45, 40–60 min: frequency 20 <div class="

Calculate frequency density for each class: 0–10: width = 10, FD = 15 ÷ 10 = 1.5 10–20: width = 10, FD = 40 ÷ 10 = 4.0 20–40: width = 20, FD = 45 ÷ 20 = 2.25 40–60: width = 20, FD = 20 ÷ 20 = 1.0 Draw the histogram with class boundaries on the x-axis (0, 10, 20, 40, 60) and frequency density on the y-axis. Each bar has no gap and its height equals the frequency density. Check: total area = (1.5 × 10) + (4.0 × 10) + (2.25 × 20) + (1.0 × 20) = 15 + 40 + 45 + 20 = 120

Exam Tips: Always calculate frequency density before drawing a histogram — never use frequency directly on the y-axis unless all class widths are equal. | When comparing box plots, write about median (location), IQR (spread), and overall range, and use comparative language such as 'higher' or 'more spread out'. | On a box plot, the whisker does not extend to an outlier — it stops at the last data point within the 1.5 × IQR boundary. | When estimating frequencies from a histogram, remember frequency = frequency density × class width (i.e. the area of the bar). | If a histogram question gives you a missing frequency, set up an equation using total area = total frequency and solve.
Common Errors: ✗ Using frequency on the y-axis of a histogram with unequal class widths ✓ The y-axis must show frequency density (= frequency ÷ class width); using frequency directly gives bars of incorrect height for unequal widths. ✗ Drawing the whisker all the way to an outlier on a box plot ✓ The whisker should end at the last data value within the 1.5 × IQR boundary; outliers are shown as separate points beyond the whisker. ✗ Saying a box plot with Q1=10, Q2=15, Q3=16 is negatively skewed because the right side of the box is shorter ✓ This is positively skewed — the median is closer to Q3, meaning the lower half of the middle 50% is more spread out, and the tail extends to the right. ✗ Calculating the
Stretch & Challenge (Grade 8-9):
  • Synoptic links: explain how histograms &amp; box plots connects to another Statistics topic you have studied
  • Real-world: research one real-world use or example of histograms &amp; box plots
  • Critical: "What are the limitations of the models used in histograms &amp; box plots?"

Plenary (5 minutes)

Assessment Criteria
  • Got it: Confident explanation + correct worked examples
  • Getting there: Main points OK, needs support with detail
  • Not yet: Confused on key concepts - re-run Lesson 2

Homework & Consolidation

Recommended Resources

🎓 Smart Lesson (Guided)