Year 6 Mathematics · AC9M6ST01

Comparing Categorical and Numerical Data Sets

Interpret distributions using mode, shape, spread and context

Ready to project and teach

Learning goalsSay it simply

Learning goal

Students identify variable type, read displays accurately and compare centre, mode, range, clusters, gaps, skew and possible extremes without claiming causes unsupported by the data.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: interpret and compare data sets for ordinal and nominal categorical, discrete and continuous numerical variables using appropriate displays; compare distributions in terms of mode, range and shape
Key conceptTeach from the board

Compare two numerical distributions

Use the visual model first. Ask students to identify the quantities, structure or conditions before calculating or explaining.

featureClass AClass Bmode1212 and 15range95shapeclustered 11–14, one high valuemore even 11–16variationgreatersmaller

One statistic does not describe a full distribution. Use several features and connect them to the measured context.

Match display to variable type

Connect the central relationship to a new context, then verify the conclusion with a second representation, estimate, inverse operation or reasonableness check.

nominal categoriescolumn graph or table
ordinal ratingsordered columns
discrete numericaldot plot or column graph
continuous numericalgrouped display or line-related context
two distributionssame scale and aligned categories

Comparisons require consistent scales and definitions. Avoid interpreting an association as a causal explanation.

Clean visual examplesOne-page board

Clean one-page examples

AC9M6ST01 - Comparing Categorical and Numerical Data Sets
Example 1

feature Class A Class B mode 12 12 and 15 range 9 5 shape clustered 11–14, one high value more even 11–16 variation greater smaller

Example 2

nominal categories column graph or table

Example 3

: determining the range for a numerical data set by finding the difference between the highest and the lowest value in the set and comparing the range for different data sets

Example 4

: representing acquired numerical data sets using side-by-side column graphs, comparing the spread of each data set using the range, the highest frequency for each data set using the mode, and discussing the shape

Curriculum examplesCopied content

AC9M6ST01: interpret and compare data sets for ordinal and nominal categorical, discrete and continuous numerical variables using comparative displays or visualisations and digital tools; compare distributions in terms of mode, range and shape

  • E1: determining the range for a numerical data set by finding the difference between the highest and the lowest value in the set and comparing the range for different data sets
  • E2: representing acquired numerical data sets using side-by-side column graphs, comparing the spread of each data set using the range, the highest frequency for each data set using the mode, and discussing the shape
  • E3: representing ordinal data collected through surveys, using visualisation tools including dot plots and bar charts, and discussing the distribution of data in terms of shape
  • E4: using technology to access data sets and graphing software to construct side-by-side column graphs or stacked line graphs; comparing data sets that are grouped by gender, year level, age group or other variables and discussing findings

Use the central and application models above to connect each elaboration to the same underlying concept.

Questions and answersWith answers

Check understanding

  • Classify a variable.
  • Find mode/range.
  • Describe shape.
  • Compare two groups.
  • Check graph scale.

Evidence of mastery

  • Represent or identify the concept
  • Explain the underlying relationship
  • Select an appropriate strategy or feature
  • Apply it in a new context
  • Justify and verify the response

Decision: continue when students can explain the model, apply it to a new example and justify their check. Otherwise return to the central model and reduce the numerical or representational load.

Practice and reviewReady for practice
Ordinal categories treated as equal numerical intervalsOrder is meaningful, spacing may not be.
Range used as complete descriptionAlso discuss concentration and shape.
Different graph scales compared visuallyRead actual values.
Cause inferred from group differenceData comparison alone does not establish cause.
Curriculum alignmentStart here

Learning goal

Students identify variable type, read displays accurately and compare centre, mode, range, clusters, gaps, skew and possible extremes without claiming causes unsupported by the data.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: interpret and compare data sets for ordinal and nominal categorical, discrete and continuous numerical variables using appropriate displays; compare distributions in terms of mode, range and shape
Related resourcesKeep teaching
Teach & ExplainTeaching slides and samples

Teach this topic step by step

Explore optional teaching slide packs for classroom lessons and explanations at home.

Browse Teach & Explain · Browse Print & Go

Teachers: follow SkillrHub on TPT, then email us to request a free sample before buying. Include the year, subject and topic or curriculum code.

Request a free sample

After trying the sample, honest feedback is welcome. A TPT review is optional, where available, and does not need to be positive.