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A little room to wonder

Statistics & Data

Calculate centre and spread, inspect unusual values and keep a sample’s limits visible.

What does a single average hide about the values behind it?

Coloured dice arranged on a dark surface.
Dice outcomes could become a dataset under a defined procedure. This photograph does not represent the fictional puzzle observations.Diacritica, via Wikimedia Commons. CC BY-SA 3.0. · Source · CC BY-SA 3.0

Start with the question and the unit

Data are recorded observations or values. Before calculating, ask what was measured, which units were used and how the records were selected. A population is the full set relevant to the question; a sample includes part of it. A convenient set of examples is not automatically representative of the wider population.

Keep categories and measurements distinct. A preferred colour is categorical data; a number of puzzle moves is numerical. A calculation should suit the kind of information, not simply every column that happens to contain a code made from digits.

Work through a fictional dataset

Five invented puzzle attempts take 4, 4, 5, 7 and 20 moves. Their sum is 40, so the mean is 40 ÷ 5 = 8 moves. In the ordered list, the middle value is 5, making the median 5. The range is 20 − 4 = 16 moves.

The mean and median answer different summary questions. The mean uses every value and is pulled towards the unusually large result. The median locates the middle of the ordered observations. Neither alone describes all five attempts, and neither labels the ability of an actual person.

Investigate an unusual value

The 20-move attempt could reflect a longer route, a different setup or a recording error. Check the context before deciding. Removing it would change the mean to (4 + 4 + 5 + 7) ÷ 4 = 5, but that numerical change does not justify deleting a valid observation.

Report the reason for any correction and preserve the original record when appropriate. A small sample can also vary by chance. If you compare two game versions, familiarity and different instructions may affect results alongside the rule you changed.

Make a graph’s choices visible

Label the variable, unit, scale and source, and mark invented data as invented. Start a bar chart’s numerical axis at zero so the bar lengths preserve relative amounts. If that hides the comparison you need, consider another chart type. Other graph types use scales differently; ask what the visual encodes.

An association between two measurements does not establish that one caused the other. Use the data to ask a better question, then identify what design or additional evidence could test the proposed explanation.

Only if you feel like trying

Show centre and spread

  1. Calculate the mean, median and range of the five invented move counts.
  2. Draw a clearly labelled display that retains all five values.
  3. Write a supported summary and one conclusion that the small dataset cannot establish.

Optional fictional data activity. No personal survey, assessment score or sensitive information is needed.