DeepMaths Junior

Junior Maths Book 1 AI Learning System

For Years 7-9 - Numbers & Statistics

Chapter 6: Data Collection and Representation

Data Collection and Representation

Choose appropriate displays and understand how data presentation affects interpretation.

Junior Maths Book 1 pages 79-1189 minutes

AI teacher

Start the short explanation, then use the visual model and practice before returning to the workbook.

Voice: Browser voice

Workbook pages

Junior Maths Book 1 pages 79-118

Use data types, surveys, frequency tables, bar charts, stem-and-leaf diagrams, grouped tables and histograms.

AI explanation

The AI teacher starts with the question being investigated, then chooses suitable data collection and display methods. Bar charts, stem-and-leaf diagrams, grouped frequency tables and histograms are compared by purpose.

  1. 1Good statistics starts with a clear question.
  2. 2Data can be discrete, continuous, categorical or grouped.
  3. 3A frequency table organises repeated values.
  4. 4A histogram uses class intervals and frequency density when class widths differ.
  5. 5A display should make the pattern easier to see, not harder.

Animated teaching

See the method

Raw data sorts into a frequency table, then changes into a bar chart and a histogram with density labels.

Score
2
4
5
7
Frequency
1
2
3
1
Bar chart with labelled frequency heights35746Frequency

Why this method works

  • Tables reduce disorder by grouping repeated information.
  • Graphs convert numbers into visible patterns.
  • Histograms use area to represent frequency, so density matters when widths change.

Common mistakes

  • Using a bar chart for continuous grouped data when a histogram is needed.
  • Forgetting labels or units on axes.
  • Treating grouped data as exact values.
  • Confusing frequency with frequency density.

Multiple methods

  • Raw data can be represented as a frequency table, stem-and-leaf diagram, bar chart or grouped display depending on the question.
  • Grouped data can be checked by total frequency.
  • Histograms can be built from frequency density or from proportional bar area.

Worked examples

Frequency table

Scores are 2, 4, 4, 5, 5, 5, 7. Make a frequency table.

Method: Count each distinct value.

  1. 1.The values are 2, 4, 5 and 7.
  2. 2.2 appears once.
  3. 3.4 appears twice.
  4. 4.5 appears three times.
  5. 5.7 appears once.

Answer: 2:1, 4:2, 5:3, 7:1

Histogram density

A class interval has frequency 12 and width 4. Find the frequency density.

Method: Use density = frequency divided by class width.

  1. 1.Frequency density = 12 divided by 4.
  2. 2.12 divided by 4 = 3.

Answer: 3

Interactive practice

Try before you look

0/3 correct, 0 answered

Question 1

Which graph is best for continuous grouped data?

Question 2

A class interval has frequency 15 and width 5. Find the density.

Question 3

What is missing if a graph has bars but no scale?

Review prompt

Explain the difference between frequency and frequency density.

Write a two-sentence answer in your notebook before marking the workbook section complete.

Challenge question

A histogram bar has width 10 and density 2.4. Find the frequency and explain why area matters.

Hint: Frequency = width x density.