IB Math AA SL Topic 4.2: Data presentation | Notes & Flashcards | Aimnova

IB Math AA SL — Data presentation

Topic 4.2 of IB Mathematics: Analysis and Approaches covers Data presentation, which is part of Unit 4: Statistics & Probability. Students explore key concepts including Frequency & histograms, Cumulative frequency, Box plots. A strong understanding of data presentation is essential for IB Math AA SL exams and builds the foundation for connected topics across the syllabus.

Key concepts in Data presentation

Key Idea: This topic is about reading data off displays — frequency tables, histograms, cumulative frequency curves and box plots — and pulling out the summary numbers (mode, median, quartiles, percentiles, IQR, outliers). It shows up as 'read off the graph' / 'find the median' questions on both papers.

📊 Tables & histograms

📈 Cumulative frequency curve

🟦 Box plots & outliers

\text{lower fence} = Q_1 - 1.5\,\text{IQR}, \qquad \text{upper fence} = Q_3 + 1.5\,\text{IQR}

$\text{IQR} = Q_3 - Q_1$: interquartile range — compute this first
$\text{outlier}$: any value beyond a fence (below lower or above upper)

✏️ IB-style worked examples

IB-style question — read a frequency table

A survey of 50 flats records the number of bicycles owned: 0 → 12, 1 → 19, 2 → 13, 3 → 6. State the mode and find how many flats own at least 2 bicycles.

Step by step:

Mode = the value with the highest frequency.
$19 \text{ flats own } 1 \Rightarrow \text{mode} = 1$
'At least 2' means 2 or 3 — add those frequencies.
$13 + 6 = 19$

Final answer:

Mode = 1 bicycle; 19 flats own at least 2.

IB-style question — median & IQR from a cumulative curve

A cumulative frequency curve for 120 students' test times is drawn (totals plotted at the upper boundaries). Reading across, the curve gives 24 min at a cumulative frequency of 60, 18 min at 30 and 31 min at 90. Estimate the median and the interquartile range.

Step by step:

Median is read from n ÷ 2.
$\tfrac{n}{2} = \tfrac{120}{2} = 60 \Rightarrow \text{median} \approx 24$
Quartiles from n ÷ 4 and 3n ÷ 4.
$Q_1 \approx 18,\quad Q_3 \approx 31$
IQR = Q₃ − Q₁.
$31 - 18 = 13$

Final answer:

Median ≈ 24 min; IQR ≈ 13 min.

IB-style question — test for an outlier (1.5×IQR rule)

A data set has Q₁ = 22 and Q₃ = 38. Determine whether a value of 65 is an outlier.

Step by step:

Find the IQR.
$\text{IQR} = 38 - 22 = 16$
Upper fence = Q₃ + 1.5 × IQR.
$38 + 1.5(16) = 38 + 24 = 62$
Compare 65 with the upper fence.
$65 > 62 \Rightarrow \text{outlier}$

Final answer:

Upper fence = 62, and 65 > 62, so 65 is an outlier.

Important: Each running total counts everything up to the top of the class, so plot it at the upper boundary, never the midpoint. Plotting at midpoints shifts the whole curve and ruins every median/quartile read.

Tap each card to reveal the answer.

Exam Tips

Mode = the data value, not its frequency; for grouped data name the modal CLASS.
Histogram bars touch (continuous); bar-chart bars have gaps (categories).
Plot cumulative totals at the UPPER class boundary, then read median at n/2, Q₁ at n/4, Q₃ at 3n/4.
For 'top X% exceed' read across from (100 − X)% of n; for 'how many between' subtract two reads.
Range = max − min; IQR = Q₃ − Q₁. Compute IQR before testing outliers with the 1.5×IQR fences.

IB Math AA SL — Data presentation

Key concepts in Data presentation

Key Idea: This topic is about reading data off displays — frequency tables, histograms, cumulative frequency curves and box plots — and pulling out the summary numbers (mode, median, quartiles, percentiles, IQR, outliers). It shows up as 'read off the graph' / 'find the median' questions on both papers.

📊 Tables & histograms

📈 Cumulative frequency curve

🟦 Box plots & outliers

\text{lower fence} = Q_1 - 1.5\,\text{IQR}, \qquad \text{upper fence} = Q_3 + 1.5\,\text{IQR}

$\text{IQR} = Q_3 - Q_1$: interquartile range — compute this first
$\text{outlier}$: any value beyond a fence (below lower or above upper)

✏️ IB-style worked examples

IB-style question — read a frequency table

A survey of 50 flats records the number of bicycles owned: 0 → 12, 1 → 19, 2 → 13, 3 → 6. State the mode and find how many flats own at least 2 bicycles.

Step by step:

Mode = the value with the highest frequency.
$19 \text{ flats own } 1 \Rightarrow \text{mode} = 1$
'At least 2' means 2 or 3 — add those frequencies.
$13 + 6 = 19$

Final answer:

Mode = 1 bicycle; 19 flats own at least 2.

IB-style question — median & IQR from a cumulative curve

Step by step:

Median is read from n ÷ 2.
$\tfrac{n}{2} = \tfrac{120}{2} = 60 \Rightarrow \text{median} \approx 24$
Quartiles from n ÷ 4 and 3n ÷ 4.
$Q_1 \approx 18,\quad Q_3 \approx 31$
IQR = Q₃ − Q₁.
$31 - 18 = 13$

Final answer:

Median ≈ 24 min; IQR ≈ 13 min.

IB-style question — test for an outlier (1.5×IQR rule)

A data set has Q₁ = 22 and Q₃ = 38. Determine whether a value of 65 is an outlier.

Step by step:

Find the IQR.
$\text{IQR} = 38 - 22 = 16$
Upper fence = Q₃ + 1.5 × IQR.
$38 + 1.5(16) = 38 + 24 = 62$
Compare 65 with the upper fence.
$65 > 62 \Rightarrow \text{outlier}$

Final answer:

Upper fence = 62, and 65 > 62, so 65 is an outlier.

Important: Each running total counts everything up to the top of the class, so plot it at the upper boundary, never the midpoint. Plotting at midpoints shifts the whole curve and ruins every median/quartile read.

Tap each card to reveal the answer.

Exam Tips

Mode = the data value, not its frequency; for grouped data name the modal CLASS.
Histogram bars touch (continuous); bar-chart bars have gaps (categories).
Plot cumulative totals at the UPPER class boundary, then read median at n/2, Q₁ at n/4, Q₃ at 3n/4.
For 'top X% exceed' read across from (100 − X)% of n; for 'how many between' subtract two reads.
Range = max − min; IQR = Q₃ − Q₁. Compute IQR before testing outliers with the 1.5×IQR fences.

IB Math AA SL — Data presentation

Key concepts in Data presentation

📊 Tables & histograms

📈 Cumulative frequency curve

🟦 Box plots & outliers

✏️ IB-style worked examples

IB-style question — read a frequency table

IB-style question — median & IQR from a cumulative curve

IB-style question — test for an outlier (1.5×IQR rule)

Exam Tips

What you'll learn in Topic 4.2

Study resources — 4.2 Data presentation

Frequency & histograms

Cumulative frequency

Box plots

Ready to study Data presentation?

Ready to practice?

IB Math AA SL — Data presentation

Key concepts in Data presentation

📊 Tables & histograms

📈 Cumulative frequency curve

🟦 Box plots & outliers

✏️ IB-style worked examples

IB-style question — read a frequency table

IB-style question — median & IQR from a cumulative curve

IB-style question — test for an outlier (1.5×IQR rule)

Exam Tips

What you'll learn in Topic 4.2

Study resources — 4.2 Data presentation

Frequency & histograms

Cumulative frequency

Box plots

Ready to study Data presentation?

Ready to practice?