Here are five scores a team put up over five matches: 2, 2, 2, 8 and 100.
Is the average score a fair way to describe this team? What would be a fairer way to say what they usually score?
Give five seconds of quiet think-time, then take three hands-up answers. The mean here (add all five scores and divide by five) is about 22.8, which describes none of the real matches — that surprise is the hook. Don't resolve it yet; hold the tension until the model step. Revoice a pupil who says "they mostly score 2" without naming the wildness of the 100.
Look at each data set below as a dot plot. The mode and range are drawn on top so you can see where each one lands.
In the last set, one dot (the 30) sits far from the rest.
Work each dot plot live — read the mode off the tallest stack, and read the range as the width from leftmost to rightmost dot. On the fourth set, cover the 30 with your hand first and have the class work out the range without it (2); then reveal it and point out the range is 25 while the tallest stack stays put. Ask "which measure changed and which stayed still?"
The fourth set is the one that pays off the hook — it shows why a single wild value can make the range misleading while the mode holds steady. On the two-mode set, head off the idea that a set must have exactly one mode.
We'll read the mode and range off the dot plot for three sets:
Talk this one through together — pupils take turns at the board and the class agrees or corrects out loud. Only the first set, {6, 6, 6, 9}, is preloaded in the interactive; type the next two sets in live at the board.
For {6, 6, 6, 9} the mode is 6, range 3 — a gentle start everyone can read. {12, 4, 15, 4, 20} makes them hunt for the repeated value (4) and compute range 16. Save {8, 8, 9, 9, 9, 40} for last: mode 9, range 32 — ask which measure the 40 stretched and which it left alone, so the outlier idea lands before the challenge round.
In your maths copy, write this data set in order from smallest to largest:
Then, side by side underneath, record its mode, its range and its mean. To find the mean, add all the values and divide by how many there are. Circle the one measure you think best describes the set.
Walk the room glancing at whether the set is genuinely in order and whether the three measures are lined up side by side — this is whole-class copybook practice, not marking. Mode 5, range 7, mean 6 (30 divided by 5); there is no single right answer to the circle, so accept any measure a pupil can justify.
Today we summarise four sets, one at a time. Read the measure asked for, then Check:
This is the practice round — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.
The practice set climbs: a clean single mode, a range with a bigger high value, another single mode, then the outlier set where the range balloons to 38 while the mode stays at 8. On the last one, before they Check, ask the class to predict whether the range will be big or small — then let the 45 make the point.
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