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
Lesson
Set out your lesson
“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.”
Bring to the table
- Two overlapping circles drawn on paper
- Counter tokens or number cards
Extra for the adult
Worked example. 6 is even and a multiple of 3, so it goes in the overlap.
Optional challenge. For Average distance from the mean, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Average distance from the mean, not mastery.
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Practice this concept
Start practiceAverage distance from the mean practice
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Learning resources
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Secondary
Before you open · source notes
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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