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Bar Charts, Pie Charts, Pictograms and Histograms — Cambridge IGCSE 0580 Maths Extended (2026)
Display and interpret data with the right chart for the data type. Cambridge tests construction (drawing) AND interpretation (reading values, comparing). Histograms are special — frequency DENSITY, not frequency.
What you’ll learn
Mapped to the Cambridge IGCSE 0580 syllabus (2025-2027).
E11.8 — Construct and interpret bar charts, pie charts, pictograms.
E11.9 — Construct and interpret histograms with equal and unequal class widths using frequency density.
Bar chart
Bars of equal width, separated by gaps. Height = frequency. For DISCRETE or categorical data.
Use for. Discrete or categorical data — number of pets, favourite subject, day of the week.
Rules.
Bars equal width.
Bars SEPARATED by small gaps (because data is discrete).
Height = frequency.
Label both axes; title the chart.
Multi-bar charts. For comparing two categories side-by-side (e.g. boys' vs girls' favourite subjects), draw paired bars with a key.
Worked. Survey of 50 students' favourite sport: football 20, tennis 15, cricket 10, swimming 5.
The HEIGHT of each bar is frequency density. The AREA of each bar (= height × width) equals the frequency.
Why? With unequal class widths, plotting frequency directly would mislead — a wide-class bar would look more important than it is. Frequency density corrects for the width.
Worked. Times to complete a task (minutes):
Class
Frequency f
Width
Frequency density
0<t≤10
8
10
0.8
10<t≤20
14
10
1.4
20<t≤40
16
20
0.8
40<t≤60
12
20
0.6
Heights: 0.8,1.4,0.8,0.6.
Note: the third class has the SAME frequency density as the first (0.8) but contains TWICE as many people (16 vs 8). This is the point of frequency density — width matters.
Reading a histogram. The frequency in any class equals (height × width). To find the number of values in a partial class (e.g. 15<t≤25), compute the area of the relevant rectangle slice.
No gaps. Bars in a histogram TOUCH (because data is continuous). Bar charts have gaps; histograms don't.
Height is frequency density, so bar AREA gives the frequency — the wide 20–40 bar holds 16 even though it is no taller than the 0–10 bar.
Continuous data.
Frequency density =f/ class width.
Height = frequency density; AREA = frequency.
Bars touch (no gaps).
Use when class widths are UNEQUAL.
Which chart for which data?
Discrete + categories: bar. Proportions of a whole: pie. Continuous: histogram. Visual / informal: pictogram.
Data type
Best chart
Discrete or categorical
Bar chart
Showing proportions of a whole
Pie chart
Continuous, equal class widths
Histogram (or frequency polygon)
Continuous, unequal class widths
Histogram with frequency density
Informal / friendly
Pictogram
Compare a few small numbers
Bar chart
Cambridge questions. Often ask "what type of chart is most suitable" — answer with the data TYPE (discrete vs continuous, equal vs unequal widths) as the justification.
Discrete / categorical: bar chart.
Proportions: pie chart.
Continuous, unequal widths: histogram.
Visual / informal: pictogram.
How it’s examined
Statistical charts appear most years — Paper 2 (3-5 marks: read or construct a simple chart) and Paper 4 (5-7 marks: histogram with frequency density and unequal widths). Examiner reports flag two errors: (i) plotting frequency instead of frequency density on a histogram when widths are unequal, (ii) angles in a pie chart not summing to 360°.
Worked examples, formulae, definitions and the mistakes examiners flag — everything you need to push from a pass to an A*.
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Download a branded revision sheet — worked examples, formulae, definitions and common mistakes for Statistical Charts and Diagrams, ready to print or save as PDF.
Step-by-step worked examples — Statistical Charts and Diagrams
Step-by-step solutions to past-paper-style questions on statistical charts and diagrams, written exactly the way a tutor would explain them at the board.
1Construct a pie chart
Core• pie chart
▼
Question
30 students chose a sport: football 12, tennis 9, hockey 6, swimming 3. Find the angle for each sector.
Step-by-step solution
Step 1
Each frequency → angle =totalfreq×360°.
Step 2
Compute.
F:3012×360=144°;T:108°;H:72°;S:36°
Answer
144°,108°,72°,36°
2Histogram with unequal classes
Extended• Adapted from 0580/42 May/Jun 2024 Q13• histogram
▼
Question
Frequency table: [0,10)=8, [10,25)=18, [25,30)=7. Find the frequency densities.
Step-by-step solution
Step 1
FD=class widthfrequency.
Step 2
Compute each.
108=0.8;1518=1.2;57=1.4
Answer
FDs: 0.8,1.2,1.4.
Examiner tip
Histogram bars use frequency DENSITY on the y-axis (not frequency) when class widths are unequal.
3Read a box-and-whisker plot
Extended• box plot
▼
Question
A box plot shows: min 4, Q1=7, median 10, Q3=14, max 20. State the median, range, and IQR.
Step-by-step solution
Step 1
Direct reads.
median=10,range=20−4=16,IQR=14−7=7
Answer
Median 10, range 16, IQR 7.
4Compare two bar charts
Extended• bar chart
▼
Question
Compare the heights of pupils in two classes shown by two bar charts.
Step-by-step solution
Step 1
Compare modal classes, ranges, or central tendency.
Answer
Use direct reads from the charts to comment on most-common heights and spread.
5Read frequencies from a bar chart
Core• Adapted from 0580/12 May/Jun 2023 Q8• bar chart, read
▼
Question
A bar chart shows the number of books read by 25 students last month: 0 books →4, 1 book →8, 2 books →7, 3 books →4, 4 books →2. State the modal number of books and the total number of books read.
Step-by-step solution
Step 1
Modal = bar with greatest frequency. Highest bar is at 1 book (8 students).
Step 2
Total books = ∑fx.
0(4)+1(8)+2(7)+3(4)+4(2)=0+8+14+12+8=42
Answer
Mode =1 book; total =42 books read.
6Compare data with a dual bar chart
Core• dual bar
▼
Question
A dual bar chart shows favourite drinks for 30 boys and 30 girls. Boys: tea 5, coffee 10, juice 15. Girls: tea 12, coffee 6, juice 12. State which drink shows the biggest difference between boys and girls, and give that difference.
Step-by-step solution
Step 1
Compute each pairwise difference: tea ∣12−5∣=7, coffee ∣10−6∣=4, juice ∣15−12∣=3.
Step 2
Biggest difference is for tea.
Answer
Tea, with a difference of 7 students.
7Draw a frequency polygon
Extended• frequency polygon
▼
Question
Frequency table of test marks: [0,10)=3, [10,20)=8, [20,30)=12, [30,40)=5. Describe the points you would plot on a frequency polygon.
Step-by-step solution
Step 1
Plot frequency against the MIDPOINT of each class.
Plot (5,3),(15,8),(25,12),(35,5) and join with straight lines.
Examiner tip
The examiner report flags candidates who plot against the lower (or upper) class boundary instead of the midpoint, losing the accuracy mark.
8Histogram with equal class widths
Extended• histogram, equal width
▼
Question
Frequency table: [0,5)=4, [5,10)=9, [10,15)=12, [15,20)=7, [20,25)=3. Each class has width 5. State the heights of the histogram bars if (a) frequency is on the y-axis, (b) frequency density is on the y-axis.
Step-by-step solution
Step 1
(a) With equal class widths, frequency on the y-axis is acceptable. Heights: 4,9,12,7,3.
Step 2
(b) Frequency density =class widthfrequency. Divide each by 5.
9Read frequency from a histogram with unequal widths (Challenge)
Challenge• Adapted from 0580/42 Oct/Nov 2024 Q11• histogram, unequal, challenge
▼
Question
A histogram has class [0,20) with frequency density 0.6, class [20,30) with FD 1.5, class [30,60) with FD 0.4. Find (a) the frequency in each class, and (b) the total number of data points.
Step-by-step solution
Step 1
Frequency =FD×class width.
Step 2
Class [0,20): width 20.
f=0.6×20=12
Step 3
Class [20,30): width 10.
f=1.5×10=15
Step 4
Class [30,60): width 30.
f=0.4×30=12
Step 5
Total.
12+15+12=39
Answer
(a) 12,15,12. (b) 39 data points.
Examiner tip
This is a classic A* trap. The examiner report consistently flags students who multiply by '1' (treating FD as frequency) or who use the wrong class width. AREA of the bar = frequency.
Key Formulae — Statistical Charts and Diagrams
The formulae you need to memorise for statistical charts and diagrams on the Cambridge IGCSE 0580 paper, with every variable defined in plain English and a note on when to use it.
Pie chart sector angle
angle=totalfrequency×360°
When to use
Constructing a pie chart.
Frequency density
FD=class widthfrequency
When to use
Histograms with unequal class widths.
Frequency from area
frequency=FD×class width
When to use
Reading a frequency from a histogram bar.
Key Definitions and Keywords — Statistical Charts and Diagrams
Definitions to memorise and the exact keywords mark schemes credit for statistical charts and diagrams answers — sharpened from recent examiner reports for the 2026 0580 sitting.
Histogram
Examiner keyword
A bar-style chart for continuous data. With unequal class widths, the y-axis is frequency density and the AREA equals frequency.
Frequency density
Examiner keyword
Frequency divided by class width. Standardises bars so that AREA represents frequency.
Pie chart
Examiner keyword
A circular chart split into sectors proportional to frequency.
Box-and-whisker plot
Examiner keyword
A summary diagram showing min, Q1, median, Q3, max.
Common Mistakes and Misconceptions — Statistical Charts and Diagrams
The traps other students keep falling into on statistical charts and diagrams questions — taken from recent Cambridge IGCSE 0580 examiner reports and mark schemes — and how to avoid them.
✕Using frequency on the y-axis of a histogram with unequal classes
0580/42 — every series
▼
Why it happens
Forgetting to convert to frequency density.
How to avoid it
Unequal classes → ALWAYS use frequency DENSITY. Bar AREA = frequency.
✕Pie sectors not summing to 360°
▼
Why it happens
Rounding errors.
How to avoid it
Check the four (or however many) sectors sum to exactly 360°. Adjust the largest by the rounding error if needed.
✕Gaps between histogram bars
▼
Why it happens
Drawing it like a bar chart.
How to avoid it
Histograms have NO gaps — continuous data, bars touch.
✕Reading the box plot's middle line as the mean
▼
Why it happens
Confusing mean and median.
How to avoid it
Box plot middle line = MEDIAN, not mean.
Practice questions
Exam-style questions with step-by-step worked solutions. Try one before checking the method.
Past paper style quiz
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4. Exam Quiz
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Video lesson
Short walkthrough of the concepts students most often get stuck on.
Statistical Charts and Diagrams — frequently asked questions
The things students keep getting wrong in this sub-topic, answered.