Average distance from the mean
Calculate the mean absolute deviation (MAD) of a small numerical data set — find the mean, find each value's distance from the mean (a non-negative number: a value equal to the mean has distance 0), then find the mean of those distances; interpret the MAD as the average distance of the values from the mean, stated in the original units of the data (e.g. minutes, cm, points); and use MADs to compare the spread or consistency of two data sets, recognising that a larger MAD means values typically sit further from the mean and that the MAD is 0 only when every value equals the mean
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Average distance from the mean 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 Average distance from the mean 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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Secondary supports Average distance from the mean. An adult previews and guides; this is a learning page, not a scored quiz.
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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
- Calculate the MAD of 4, 6, 8, 9, 13 (mean 8; distances 4, 2, 0, 1, 5; MAD 2.4), counting the value equal to the mean as a distance of 0
- Explain that a MAD of 3 cm for a set of plant heights means the heights are, on average, 3 cm away from the mean height
- Decide which of two bowlers, both with a mean score of 120, is more consistent when their MADs are 8 and 21 points, and justify the choice
“If your child wrote down how many minutes late the school bus was each day for a week, could they work out how far each day was from the average lateness, average those distances, and explain what that number says about how reliable the bus is?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Data & Statistics
- Age range
- Ages 11–12
Standards