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Analysing Datasets and Drawing Conclusions
Rung 2 of 4 · The method

Centre, Spread, Shape — Then Conclude

Every fair description of a dataset has the same three moving parts. Get into the habit of naming all three and a tidy conclusion almost writes itself.


PractiseRead the dot plot, then call the centre, spread and shape. The toy stitches your three picks into a fair conclusion.
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There's a recipe for describing any dataset, and it's only three steps. Centre, spread, shape — in that order — then put them in a sentence.

Step 1 — Centre: What's a Typical Value?

Quote the mean or the median — whichever is fairer. If the data is bunched up evenly, they'll sit close together and either is fine. If there's a long tail or an outlier dragging things, the median is the honest "typical". For 3, 4, 4, 5, 5, 5, 6 the mean and median both land near 5 — so "a typical value is about 5" is fair either way.

Step 2 — Spread: How Varied Is It?

Reach for the range — biggest minus smallest. A small range means everyone's similar (consistent); a big range means the values are all over the place. For that same list, 6 − 3 = 3, a fairly tight spread. Saying "the range is 3, so the results are pretty consistent" already tells the reader something the average can't.

Step 3 — Shape: How Do the Dots Sit?

Glance at the dot plot. Are they clustered in one lump, spread evenly along the line, or skewed — most values down one end with a tail trailing off the other way? Skew is the big tell: when the data has a tail, the mean gets tugged toward it, which is exactly why you'd quote the median instead.

Say it plainly: describe every dataset in three moves — centre (mean or median), spread (range), shape (clustered / spread / skewed). Then write one sentence that names all three.

Worked Example — Putting It Together

Suppose the data is 2, 2, 3, 3, 3, 4, 9. The mean is about 3.7 but the median is 3 — they disagree, a clue something's pulling the mean. The range is 9 − 2 = 7, and the dot plot shows a cluster low down with one lonely 9 off to the right: skewed. So a fair conclusion reads: "Most values sit around 3 (the median), the data is fairly spread (range 7) and it's skewed by one high value, so the median describes it better than the mean." That single sentence covers centre, spread and shape — and it's honest.

Us, Thinking Out Loud

Could you describe a dataset to me using all three — centre, spread, shape?

How do you decide whether to quote the mean or the median?