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MathematicsData & StatisticsAges 11–13

Describing distributions

Describe the distribution of a numerical data set by its centre, spread and overall shape — recognising clusters, gaps, peaks, symmetry or skew (a longer tail on one side) and unusual values — and interpret each feature in the context in which the data were collected, recognising that distributions with similar centres can differ greatly in spread and shape

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Describing distributions means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.

Materials: Two overlapping circles drawn on paper; Counter tokens or number cards. 1. Say the goal of Describing distributions in plain words once. 2. Adult sorts numbers into A, B, both, or neither for “even” and “multiple of 3”. 3. Child sorts three sets into a Venn diagram and counts each region. 4. Fresh check: one fresh item placement in the overlap. Record and stop. Done: three correctly sorted Venn diagrams with region counts. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.

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Describing distributions practice

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Secondary supports Describing distributions. An adult previews and guides; this is a learning page, not a scored quiz.

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Ask the learner one fact they learned and one question they still have.

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Public NRICH page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.

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Check understanding

  • Describe a dot plot of 25 pupils' reaction times by its centre (a typical value), its spread (where most values lie and how far they extend) and its shape — naming any cluster, gap, symmetry or skew and unusual value — and link each feature to the context (e.g. a gap between two groups of times might reflect pupils who had practised and pupils who had not)
  • Compare two distributions with the same mean — e.g. two classes both averaging 60% on a test, one with scores clustered between 52% and 68%, the other spread from 20% to 95% in two separate clusters — and explain what the shared mean hides and why the difference matters in context
  • Use the context to judge whether an unusual value is more likely a recording error or a genuine extreme (e.g. a reaction time of 4.2 s among times near 0.3 s), and identify claims the display alone cannot support, such as the reason for a skew or that the same pattern would hold for a different group
“If your child sees a dot plot of how long children in their class took to run 100 m, could they describe where most times bunch up, how spread out they are and whether there are any odd ones out — and suggest a sensible reason for what they see?”

Curriculum record

Type
Conceptual
Subject
Mathematics
Domain
Data & Statistics
Age range
Ages 11–13

Standards

acara-v9:AC9HS6S03acara-v9:AC9M6ST01ccss-math:6.SP.2ccss-math:6.SP.5cthe-ontario-curriculum-mathematics-2020:ON-MATH-2020-G6-D1.6the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G7-D1.5the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G7-D1.6uk-nc-2013:KS3.Maths.Stat.1