IB Maths Descriptive Statistics: FAQ

According to the IB Mathematics guide (first exams 2021, still current for the 2025 cohort under the same Topic 4 structure), this content sits under 'Statistics and probability' — Topic 4.1–4.3 for both AA and AI. Expect:

• A grouped frequency table question requiring mean and standard deviation from mid-interval values
• A cumulative frequency graph used to estimate median and IQR
• A GDC-based one-variable statistics calculation (1-Var Stats)

Quick tip: examiners regularly award a mark just for correctly reading GDC output — practise reading it, not just generating it.

Worked example: data set 2, 4, 4, 6.

1. Mean $=\frac{2+4+4+6}{4}=4$
2. Squared deviations: $4, 0, 0, 4$
3. Variance $=\frac{8}{4}=2$
4. Standard deviation $=\sqrt{2}\approx 1.41$

Common mistake: students report variance when the question asks for standard deviation, or forget the GDC gives you ${\sigma }_x$ directly under 1-Var Stats — no need to square-root by hand.

Steps for a data set of 80 students:

1. Median position: $\frac{80}{2}=40$th value — read across from 40 on the cumulative frequency axis
2. Lower quartile: $\frac{80}{4}=20$th value
3. Upper quartile: $\frac{3\times 80}{4}=60$th value
4. IQR $=$ upper quartile $-$ lower quartile

Quick tip: draw the horizontal line to the curve, then straight down — examiners often award a method mark just for correct graphical technique, even if the final read-off is slightly off due to graph scale.

The real divergence between AA and AI in the statistics topic shows up later, in correlation, regression and probability distributions — not in Topic 4.1–4.3's descriptive measures. If you're choosing between AA and AI, don't let descriptive statistics be the deciding factor since it's the same either way.

Checklist before you submit any descriptive statistics answer:

1. Did you state which GDC function you used (or show the formula)?
2. Did you round to 3 s.f. as the IB default requires, unless the question specifies otherwise?
3. Did you include correct units (cm, kg, USD) if the context demands it?
4. For grouped data, did you use mid-interval values, not the raw class boundaries?

Quick tip: on Paper 2, always check whether the question wants the sample standard deviation ($s_{n-1}$) or population standard deviation (${\sigma }_n$) — the GDC gives both, and picking the wrong one is one of the most common silent mark losses I see.

Practical steps (TI-84 example):

1. STAT → Edit → enter data into L1 (and frequencies into L2 if grouped)
2. STAT → CALC → 1-Var Stats → specify L1, L2
3. Read off $\bar{x}$, ${\sigma }_x$ (population), $s_x$ (sample), median, Q1, Q3

Common mistake: entering raw class boundaries instead of mid-interval values for grouped data, which silently skews the mean. RevisionPrep's Topical Worksheets on statistics include GDC-input drills specifically to build this speed before exams.

Don't treat this topic as low-stakes because the direct mark allocation looks small. In my experience examining mock papers, students who are shaky on standard deviation and IQR consistently lose extra marks two or three questions later, once the same skill resurfaces inside a probability distribution or correlation question.

Common mistake: rounding too early. If you round the mean to 3 s.f. and then use that rounded value to calculate standard deviation by hand, your final answer drifts from the GDC's exact value — examiners do notice and can withhold accuracy marks for premature rounding.

The formula booklet (current for both subjects) lists $\sigma =\sqrt{\frac{\sum (x-\bar{x}{)}^2}{n}}$ under the Topic 4 section. Bring your own clean copy into the exam — annotating a shared or previous-year copy is against IB exam regulations.

The fix is usually targeted practice with real IB-style grouped-data and cumulative-frequency questions, not more algebra revision. RevisionPrep's Topical Worksheets for Maths statistics are built around exactly this — repeated GDC-entry drills alongside interpretation questions, which is where most marks are actually lost.

On RevisionPrep, the Revision Notes cover the formula and concept side, the Topical Worksheets isolate descriptive statistics for repeated practice, and the Mock Papers put it back into full exam context alongside other topics — which is where students discover whether they're actually fast enough under time pressure.