IA statistics, step by step · Cleaning data and outliers

Cleaning data and outliers in a Maths IA: the 1.5 × IQR rule

AA SLAA HLAI SLAI HL

Raw data are messy. This page finds the outliers in a real-looking data set with the 1.5 × IQR rule, then shows why each one needs its own decision — and how to justify it in your write-up.

Guidance based on the checklist Pete Bromfield — an IB examiner and former Head of Maths — uses with his own students. Not affiliated with or endorsed by the IB.

Example data, invented for this guide. The context is realistic, but the numbers were made up to show the method. Use your own collected or sourced data in your IA.

When to use it

Before any calculation: as soon as your data are in a spreadsheet.
When a value looks impossible, or very far from the rest.
When you combine data from different sources or people.

Course fit: Every course. The IB defines an outlier as a value more than 1.5 × IQR below the lower quartile or above the upper quartile; box plots and quartiles are in the SL core of AA and AI.

The example data

25 students typed their usual door-to-door journey time to school into an online form. One answer is 450 minutes; another is 95 minutes.

12, 15, 18, 20, 22, 22, 25, 25, 26, 28, 30, 30, 32, 33, 35, 35, 38, 40, 42, 45, 48, 50, 55, 95, 450 (min)

The raw data: finding the outliers

First the summary of the data exactly as they arrived, with the fences of the 1.5 × IQR rule.

Step 1 · Put the 25 values in order

12, 15, 18, 20, 22, 22, 25, 25, 26, 28, 30, 30, 32, 33, 35, 35, 38, 40, 42, 45, 48, 50, 55, 95, 450

n = 25. Ordering first makes the median, the quartiles and any outliers easy to see.

Step 2 · Centre: mean and median

x̄ = Σx / n = 1271 / 25 = 50.84

Median: the middle value of the ordered list (value number 13) = 32.00.

Box plot of journey time to school for the raw example data, with outliers marked — Raw data: the box spans the quartiles, the whiskers reach the furthest values inside the fences, and open circles are outliers by the 1.5 × IQR rule.

In the full worked analysis

The rest of the working: steps 3 to 4
After cleaning: one value corrected, one kept
What the example shows, in context
On a GDC: TI-84 Plus CE, TI-Nspire CX and Casio fx-CG50
What examiners look for
Common mistakes
Limitations to discuss

How this maps to the IA criteria

A Criterion A (Presentation): Cleaning described in a short, clear paragraph before the analysis, with raw data in an appendix.
B Criterion B (Mathematical communication): Fences shown with their calculation, outliers marked on the box plot.
C Criterion C (Personal engagement): Decisions based on knowing your own data and context — the kind of thinking examiners reward.
D Criterion D (Reflection): Reflecting on how each decision changes the results and the conclusion.
E Criterion E (Use of mathematics): Quartiles, IQR and fences calculated correctly, with the method stated.

These are the current criteria A–E, for exams up to November 2028. For the new courses (first assessment May 2029) the IB has confirmed one set of four criteria for SL and HL: A Problem specification (4 marks), B Abstraction (6), C Computation (4) and D Interpretation (6), still 20 marks and 20% of the grade at both levels — see the IB's new AA and AI subject briefs. The detailed descriptors come with the new guide; check with your teacher which criteria apply to you. The advice is our summary, not the IB's wording.

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Frequently asked questions

What counts as an outlier in an IB Maths IA?

The IB's definition: a value more than 1.5 × IQR below the lower quartile or above the upper quartile. Use it to identify outliers, then decide what to do with each one.

Should I remove outliers from my IA data?

Only with a reason. Correct checkable errors, remove impossible values or values from outside your population, and keep genuine unusual values — saying what they do to your results.

Does removing outliers lose marks?

Removing them without a reason can. Explaining a sensible decision and showing its effect is good reflection (Criterion D).

Next steps

Related: Descriptive statistics and box plots · Sampling and collecting data. Or analyse your own data, find a data set in the IA data bank, and see what the IA package adds.

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