Did you know that a number which looks wrong can be the most informative part of a school experiment? A learner sees four similar measurements and one unusually large reading. Crossing out the last one makes the table tidier—but may also erase the observation the investigation needed to notice.
An outlier is an observation that stands noticeably apart from the rest of a dataset. Before excluding it, investigate whether it came from a recording mistake, a measurement problem, a different kind of object, or a genuine result. Keep the original entry, record the reason for any correction or exclusion, and compare conclusions with and without the unusual value when useful.
Start with the question, not the most attractive average
A science table is evidence about something specific: perhaps the height of five seedlings measured in centimetres on the same day. If the task concerns those five seedlings, a surprisingly tall seedling is not automatically disqualified. If it concerns seedlings from one identical treatment group and a pot was accidentally mixed in from another group, the group definition may matter more than how tall the plant is.
Before calculating, ask a pupil to identify the object, measurement, unit, date, sampling rule and original observation record. Can the pupil explain why the apparently unusual reading belongs in this table? That answer is a stronger diagnostic than asking the child simply to circle the largest number.
Worked example: the 52-centimetre seedling
Consider an invented example, not actual pupil data. Five recorded seedling heights are 11 cm, 12 cm, 12 cm, 13 cm and 52 cm. The four shorter heights cluster together; 52 cm deserves checking, but its size alone cannot tell us whether it is wrong.
- Mean using all five: (11 + 12 + 12 + 13 + 52) ÷ 5 = 100 ÷ 5 = 20 cm.
- Median using all five: the middle of the ordered values is 12 cm.
- Difference: the mean is 8 cm above the median because the single large reading strongly influences the sum.
- If original evidence confirms a transcription error: suppose a dated field sheet actually says 12 cm, not 52 cm. The corrected values total 60 cm, so the corrected mean is 12 cm.
Notice the essential condition in that last line: we are allowed to correct 52 to 12 only because an original record verified the transcription mistake. We cannot simply replace it with a convenient number because the corrected average looks nicer.
Three different causes require three different responses
1. A demonstrable recording error
If the measuring sheet says 12 cm but the spreadsheet says 52 cm, preserve a correction note: ‘Original sheet checked; spreadsheet entry corrected from 52 cm to 12 cm.’ Retain the audit trail so another person can reproduce the decision. A correction repairs data rather than manufacturing a new result.
2. A genuine but non-comparable observation
Suppose the 52 cm plant came from a different age group that was accidentally included. If the stated investigation only covers seedlings aged two weeks, the older plant may belong in a separate record. Explain the eligibility rule and show both the original table and the analysis of the intended group. Do not invent the age after seeing the number.
3. A genuine observation from the intended group
If a careful recheck supports 52 cm and it belongs to the same group, retain it. Report how sensitive the mean is and consider also describing the median and the full range. You can investigate why this plant is different without claiming a cause the experiment has not established.
The US National Institute of Standards and Technology explains that a conspicuous observation can reflect erroneous data, natural variation or something scientifically interesting. It distinguishes investigating an unusual point from routinely deleting it.
A four-step learner diagnostic
- Name: Can I state precisely what was measured and for which objects?
- Trace: Can I find the original dated notebook, image or instrument record for the unusual entry?
- Classify: Do I have evidence for an error, a non-comparable case or a valid unusual result—or is the cause unknown?
- Report: Can I show what I kept or changed, why, and how the result affects my conclusion?
An instructive warning sign is the sentence ‘We removed 52 because everyone else’s result was about 12.’ That gives a reason for noticing it, not evidence for rejecting it. Ask, ‘Which record proves 52 was invalid?’ If the learner cannot point to one, label the reading ‘unusual; requires investigation’, not ‘wrong’.
Progressive practice: guided, paired, independent
Guided: Put the five invented heights on a number line. Let the tutor model the original mean and median, then read a hypothetical dated sheet confirming a copying error. Explain what changes and what remains in the audit trail.
Paired: Give learners a second fictional dataset: 8 cm, 9 cm, 9 cm, 10 cm and 34 cm. The total is 70 cm; the mean is 14 cm and the median is 9 cm. One learner argues for keeping 34; the other asks what information would justify excluding it. Neither may decide merely from the size.
Independent: A new table lists five values, one unusual. Without hints, the learner must write the original summary, two plausible causes, an evidence check, and a justified decision. A parent or tutor should look for the argument rather than a rehearsed sentence.
What improvement should look like
Progress is observable when the child stops silently erasing inconvenient values, labels units consistently, shows both mean and median when appropriate, checks the source record and explains why a data decision is justified. A useful quick check is to swap in a new dataset and ask whether the same reasoning transfers. A perfectly neat chart alone does not demonstrate that understanding.
For parents and teachers: protect the record, not just the mark
Parents can ask: ‘What did you actually observe?’ and ‘How could we check that unusual number?’ Teachers can require a short annotation for every corrected or excluded point, including the evidence used. Avoid turning the exercise into a lesson that outliers are always bad; a small classroom sample may simply contain natural differences.
Limits and frequently asked questions
Should a school child calculate a formal outlier test?
Usually the first priority is understanding the measurement, verifying entries and explaining the consequence for the conclusion. Formal statistical tests have assumptions and may not be suitable for five classroom readings. Do not treat a generic cutoff as a substitute for investigating the cause.
Does the median always tell the truth better than the mean?
No. Both describe different aspects of a dataset. The median resists the influence of one extreme value, while the mean uses every numerical value. The right summary depends on what the question asks, the sampling process and the shape of the data.
What if we cannot remeasure?
Preserve the original value, disclose the uncertainty and, if helpful, present sensitivity analyses with and without the point without declaring either one the uniquely correct result. Do not invent a replacement value.
Build the habit beyond one science table
The next step is learning to select a measurement that answers the investigation question and to record uncertainty honestly in a nature journal. For a wider framework, explore How Education Works and eduKateSG’s explanation-first Mathematics tutorial approach. A learner who can defend one unexpected observation is learning something more durable than how to produce a pleasing average.