Outliers and fair conclusions | Year 11

01 / LEARN

The idea, step by step

A flag starts an investigation

One common rule flags values below $Q_{1} - 1.5 I Q R$ or above $Q_{3} + 1.5 I Q R$ . Use the stated quartile convention. A flagged value is distant from the middle, but the rule does not prove an error.

Check original records, units and population definitions. A 160-minute trip could be genuine; 1600 might be a transcription error. Evidence, not a preferred mean, should guide treatment.

Show sensitivity honestly

Correct and document verified errors. Explain any defensible pre-established exclusion rule. Otherwise retain relevant genuine observations and choose suitable summaries, or show a sensitivity analysis with and without the extreme.

Extremes can strongly change mean and range while leaving median/IQR relatively stable. They may reveal a real subgroup or important event. Removing them silently can misrepresent the group.

A common trap

Delete everything outside the fences.

Instead: A fence flags an observation to investigate, not a mandatory deletion.

02 / WORKED EXAMPLES

See the thinking

Example 1

Find fences

Q1=10, Q3=18. Test−3 and 31.

IQR 8.
Fences $10 - 12 = - 2$ and $18 + 12 = 30$ .
−3 and 31 are outside.

Both flagged; neither automatically wrong.

Example 2

Sensitivity

Compare 4, 5, 5, 6, 30 with and without 30.

With all: mean 10, median 5.
Without 30: mean 5, median 5.
Mean changes greatly; median does not.

Exclusion changes mean 10 to 5 but still needs a valid reason.

Check your understanding

Q1=6, Q3=10. Upper fence?

Show answer

16.

IQR 4; $10 + 1.5 (4) = 16$ .

03 / WORKSHEET

Your turn

6 questions · 12 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Find fences for Q1=12, Q3=20.
2 marks
A value equals the upper fence 32. Is it flagged by the strict outside rule?
2 marks
Source confirms 1.75 m entered as 1.75 cm. What correction?
2 marks
Find mean and median of 3, 4, 4, 5, 24.
2 marks
Slow runners are removed to improve mean race time. Explain the problem.
2 marks
Results change greatly without one genuine extreme. What should be reported?
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Find fences for Q1=12, Q3=20.
2 marks
IQR 8; subtract/add 12.
0 and 32.
A value equals the upper fence 32. Is it flagged by the strict outside rule?
2 marks
The rule uses values above, not equal to, the fence.
No.
Source confirms 1.75 m entered as 1.75 cm. What correction?
2 marks
It is a verified unit mismatch.
175 cm, documenting the unit correction.
Find mean and median of 3, 4, 4, 5, 24.
2 marks
Total 40 divided by count 5; third value 4.
Mean 8; median 4.
Slow runners are removed to improve mean race time. Explain the problem.
2 marks
Exclusion cannot be justified by wanting a nicer result.
Selective removal of genuine outcomes biases the description.
Results change greatly without one genuine extreme. What should be reported?
2 marks
Readers need to see the sensitivity.
Both relevant results, the treatment rule and a cautious conclusion.

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Curriculum reference & lesson scope

SACE Board of South Australia

Stage 1 General Mathematics: statistical investigation, univariate data, sampling, displays, summaries and interpretation.

Official curriculum source ↗

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