Understand the idea.
A flag starts an investigation
The rule flags a value below or above . Calculate the quartiles using the stated convention. Values equal to a fence are not outside it.
A flag identifies distance from the central data; it does not diagnose an error. Check the original response, units and intended population. A genuine long journey may be important evidence about the group.
Show sensitivity honestly
Correct verified recording errors and document the evidence. Use a defensible, stated exclusion rule when one applies. Do not remove a valid observation simply because it changes the conclusion or makes an average less attractive.
A sensitivity analysis shows results with and without a questionable extreme, explaining the distinction. Mean and range can shift sharply while median or IQR change less. Both calculations describe different sets of observations and must be labelled.
See the method in action.
Find fences
Q1=10, Q3=18. Test−3 and 31.
Worked solution
- 1
Calculate the IQR.
The central spread determines the distance used beyond each quartile.
- 2
Calculate both fences.
The rule extends one and a half IQRs below and above the central half.
- 3
Compare each value with the fences.
Both values lie strictly outside the permitted fence interval.
- 4
State the appropriate response.
Flag both observations for checking; neither comparison proves that the recorded value is wrong.
Both flagged; neither automatically wrong.
Sensitivity
Compare 4, 5, 5, 6, 30 with and without 30.
Worked solution
- 1
Summarise all five values.
The full data total fifty, and the third ordered value is five.
- 2
Summarise the four values without thirty.
Removing one value changes both the total and the count.
- 3
Compare the sensitivity.
The mean drops by five while the median is unchanged, showing that the high value strongly affects the mean.
- 4
Separate the calculation from the decision.
A lower mean is not itself a valid reason to exclude thirty; any exclusion needs evidence or a defensible rule.
Exclusion changes mean 10 to 5 but still needs a valid reason.
Try it yourself.
Check your understanding
Q1=6, Q3=10. Upper fence?
Show answer & reasoning
16.
First find . The upper fence is . It begins at the upper quartile, not at the median.
Keep practising
6 worksheet questions · 12 marks
Read the questions online
- Find fences for , .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 , .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.
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 ↗