Statistical Analysis Vocabulary

Activities to try

1. 1

   Draggable data set: watch the measures behave differently

   Why it works: Mean, median and mode are not interchangeable words for 'average': they track different things, and seeing them respond differently to the same change is what pulls the words apart. The mean is influenced by every value, so an outlier drags it while the median hardly moves; range is a single distance; correlation names the direction of a trend, not a cause.

   1. Start with a small, meaningful data set shown as dots on a value strip — e.g. goals a team scored across seven matches: 2, 0, 1, 3, 2, 2, 8 (ordered: 0, 1, 2, 2, 2, 3, 8, so the mode is a single clear value, 2).
   2. Read the mean, median, mode and range displayed and labelled live beside the data, each with a one-line 'what it tells us'.
   3. Drag one match's score (say the 3) up to 20 and watch the mean slide up to chase it, the median barely move, and the mode stay unchanged — the moment the three labelled numbers behave DIFFERENTLY.
   4. Drag a value far from the rest to create an outlier, then recompute the mean with and without it and compare how little the median shifts.
   5. See the range marked on a number line as the labelled distance from lowest to highest, so it reads as one number, not two.
2. 2

   Narrate the data: use the words for the right thing

   Why it works: Owning the vocabulary means using each word for the thing it names when describing freely — not reciting definitions. Narrating real data exposes and corrects swaps (mode called 'average', range given as two numbers, correlation slid into cause) that a definition task would let a child recite around.

   1. Take a small real data set — e.g. 2, 0, 1, 3, 2, 2, 8 — and a scatter graph of height against shoe size, and tell the story of the data aloud using mean, median, mode and range as you go.
   2. For each term, say not just the value but what it tells us: the mode is the most frequent value (2, appearing three times); the median is the middle AFTER ordering (2); the mean (≈2.57) is a typical / fair-share score; the range is 8, the difference 8−0.
   3. Name the 8 as an outlier and say what it does — it drags the mean UP while the median barely moves.
   4. Describe the scatter with the right word: 'positive correlation' meaning taller children tend to have bigger feet — a link, not a cause.
   5. Answer follow-up probes: 'What does that 2.57 actually tell us about how this team scores?'; 'Why did you have to order the numbers for the median but not the mode?'; 'If that 8 had been 80, which number would change most and which hardly at all?'; 'Does being tall MAKE feet grow, or is there a word for the link without saying one causes the other?'
3. 3

   Match and sort: check correct use, not definitions

   Why it works: Correct use can be probed by matching and categorising against a data context — this surfaces swaps without asking the child to recite a definition.

   1. On a given ordered data set, match each word — mean, median, mode, range — to the value it names.
   2. Sort a set of scatter graphs into positive / negative / no correlation.
   3. Choose which sentence uses 'range' correctly, where a distractor names the two extreme values ('0 and 8') instead of their difference (8).
   4. Judge statements as 'uses the word correctly' or 'incorrectly' (e.g. 'the median is the middle of the unordered list', 'the mode is the average').