What are the different types of statistical charts and diagrams used in Cambridge IGCSE Mathematics?

In Cambridge IGCSE Mathematics, students commonly use various statistical charts and diagrams such as bar charts, pie charts, histograms, line graphs, and scatter plots. Each type serves a specific purpose: bar charts are used for comparing quantities, pie charts show proportions, histograms display frequency distributions, line graphs track changes over time, and scatter plots illustrate relationships between two variables.

How do you interpret a histogram in IGCSE Statistics?

In IGCSE Statistics, a histogram is interpreted by analyzing the frequency of data within certain intervals, known as bins. The height of each bar represents the frequency of data points within that interval. Unlike bar charts, histograms have no gaps between bars, indicating continuous data. By examining the shape of the histogram, students can identify patterns such as skewness, modality, and the spread of the data.

What is the difference between a bar chart and a histogram in statistical diagrams?

The primary difference between a bar chart and a histogram lies in the type of data they represent. Bar charts are used for categorical data and have gaps between bars, while histograms are used for continuous data and have no gaps between bars. Bar charts compare different categories, whereas histograms show the distribution of numerical data across intervals.

Why are pie charts useful in representing statistical data?

Pie charts are useful in representing statistical data because they visually display the proportions of a whole. Each 'slice' of the pie represents a category's contribution to the total, making it easy to compare relative sizes. This makes pie charts particularly effective for showing percentage distributions and highlighting the largest or smallest segments within a dataset.

How can scatter plots help in understanding relationships between variables in IGCSE Mathematics?

Scatter plots are valuable in IGCSE Mathematics for understanding relationships between two variables. By plotting data points on a Cartesian plane, students can visually assess whether there is a correlation between the variables. Patterns such as positive, negative, or no correlation can be identified, helping to determine the strength and direction of the relationship. Scatter plots are also useful for identifying outliers and trends within the data.

Why is "Using frequency on the y-axis of a histogram with unequal classes" a common mistake in Statistical Charts and Diagrams?

Why it happens: Forgetting to convert to frequency density. How to avoid it: Unequal classes → ALWAYS use frequency DENSITY. Bar AREA = frequency. Source: 0580/42 — every series

Why is "Pie sectors not summing to $360\degree$" a common mistake in Statistical Charts and Diagrams?

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.

Why is "Gaps between histogram bars" a common mistake in Statistical Charts and Diagrams?

Why it happens: Drawing it like a bar chart. How to avoid it: Histograms have NO gaps — continuous data, bars touch.

Why is "Reading the box plot's middle line as the mean" a common mistake in Statistical Charts and Diagrams?

Why it happens: Confusing mean and median. How to avoid it: Box plot middle line = MEDIAN, not mean.

Cambridge IGCSE Mathematics (0580)

Statistical Charts and Diagrams

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Short Notes - Statistical Charts and Diagrams

Detailed Study Notes

Detailed notes on Statistics for Cambridge IGCSE Mathematics, covering key concepts, explanations, examples, and exam-focused revision points.

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.

At a glance

Bar chart: bars of equal width for discrete categories.
Pie chart: angles in proportion to frequencies; total $360\degree$ .
Pictogram: a symbol represents a fixed number; key needed.
Histogram: bars represent CONTINUOUS data; bar AREA $=$ frequency.
Frequency density $= \dfrac{\text{frequency}}{\text{class width}}$ .
Use histograms when class widths are UNEQUAL.

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 $5$ .

Four bars of equal width, heights $20, 15, 10, 5$ .
Gaps between bars.
$y$ -axis labelled "Frequency", $x$ -axis labelled "Sport".

Equal-width bars with gaps — bar height reads off the frequency.

Discrete / categorical data.
Bars equal width, with gaps.
Height = frequency.
Label axes and title.

Pie chart

Angle of each sector $= \dfrac{\text{frequency}}{\text{total}} \times 360\degree$ .

Use for. Showing how a whole is split into proportions.

Construction.

Compute the total frequency.
Each category's angle: $\theta = \dfrac{f}{\text{total}} \times 360\degree$ .
Draw a circle. Use a protractor to mark each angle.
Label each sector with the category and (optionally) the angle or percentage.

Worked. Same survey: football $20$ , tennis $15$ , cricket $10$ , swimming $5$ . Total $50$ .

Football: $\dfrac{20}{50} \times 360 = 144\degree$ .
Tennis: $\dfrac{15}{50} \times 360 = 108\degree$ .
Cricket: $\dfrac{10}{50} \times 360 = 72\degree$ .
Swimming: $\dfrac{5}{50} \times 360 = 36\degree$ .
Check: $144 + 108 + 72 + 36 = 360\degree$ . ✓

Each sector angle is proportional to its frequency; all angles sum to 360°.

Reading a pie chart. If you know the total and the angle, the frequency is $\dfrac{\theta}{360} \times \text{total}$ .

Cambridge tip. Mark schemes credit a clear angle calculation table — even if the drawing is rough.

Angle $= \dfrac{f}{\text{total}} \times 360\degree$ .
All angles must sum to $360\degree$ .
Reading: $f = \dfrac{\theta}{360} \times \text{total}$ .
Show the angle table as working.

Pictogram

A symbol represents a fixed number of items. Key required.

Use for. Visually appealing, easy-to-grasp summaries — especially when numbers are small or for younger audiences.

Rules.

Each symbol represents a fixed number (the key).
Half-symbols (or quarters) represent fractions of the key value.
KEY MUST BE SHOWN.

Worked. Pictogram of class books read this term, where each book symbol $= 4$ books:

Anna: $\bigstar \bigstar \bigstar = 12$ books.
Ben: $\bigstar \bigstar \frac{1}{2}\bigstar = 10$ books.
Carol: $\bigstar \bigstar \bigstar \bigstar = 16$ books.

Reading. Multiply the number of full symbols (plus fractions) by the key value.

Cambridge tip. Always SHOW the key — Cambridge mark schemes deduct for missing keys.

One symbol = fixed number (the key).
Half-symbol = half the key value.
Key must be drawn / labelled.

Histogram (with frequency density)

Bar AREA $=$ frequency. Use FREQUENCY DENSITY ( $f /$ class width) when class widths are unequal.

Use for. Continuous data, especially with UNEQUAL class widths.

Key formula. $\text{frequency density} = \dfrac{\text{frequency}}{\text{class width}}.$

The HEIGHT of each bar is frequency density. The AREA of each bar (= height $\times$ 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
$0 < t \le 10$	8	10	0.8
$10 < t \le 20$	14	10	1.4
$20 < t \le 40$	16	20	0.8
$40 < t \le 60$	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 $\times$ width). To find the number of values in a partial class (e.g. $15 < t \le 25$ ), 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.

Quick recap

Bar chart: discrete / categorical, gaps between bars.
Pie chart: angle $= \dfrac{f}{\text{total}} \times 360\degree$ .
Pictogram: key required.
Histogram: continuous, frequency density on $y$ -axis.
Histogram: bars touch; AREA = frequency.
Pick the chart for the DATA TYPE.

Memorise this

Verbatim phrases and definitions Cambridge mark schemes credit.

Bar chart — equal-width bars with gaps, for discrete or categorical data.
Pie chart — circular chart with sectors proportional to frequencies.
Pictogram — symbols representing fixed values; key required.
Histogram — bars representing continuous data; bar area equals frequency.
Frequency density — frequency divided by class width.

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 $360\degree$ .

Sources: Cambridge IGCSE Mathematics 0580 syllabus 2025-2027 (E11.8-11.9); 0580/42 Oct/Nov 2024 — Q18 (histogram, unequal widths); 0580 Examiner Reports 2022-2024. Last reviewed 2026-05-05.

Take this whole topic with you

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.

Question type:

Question patterns to master — Statistical Charts and Diagrams

Almost every statistical charts and diagrams exam question is one of these shapes. Learn to spot each one and you will always know how to start.

Graph or diagram

Recognise it by

The whole question is built around a chart — construct a pie chart, draw a histogram / frequency polygon, or read / compare a bar chart or box-and-whisker plot.

How to approach it

Match the chart's rule: pie sector $= \tfrac{\text{freq}}{\text{total}} \times 360\degree$ ; histogram height $=$ frequency density $\tfrac{\text{freq}}{\text{class width}}$ for unequal classes; frequency polygon points plotted at class midpoints; box plot read directly for median, range and IQR.

Common trap

Examiner reports flag putting frequency (not frequency density) on a histogram with unequal classes, plotting frequency polygons against a class boundary instead of the midpoint, drawing gaps between histogram bars, and reading the box plot's middle line as the mean rather than the median.

1Construct a pie chart
CoreGraph or diagram• 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
1. Step 1
  Each frequency $\to$ angle $= \dfrac{\text{freq}}{\text{total}} \times 360\degree$ .
2. Step 2
  Compute.
  $F: \dfrac{12}{30} \times 360 = 144\degree;\ T: 108\degree;\ H: 72\degree;\ S: 36\degree$
Answer
$144\degree, 108\degree, 72\degree, 36\degree$
2Histogram with unequal classes
ExtendedGraph or diagram• 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
1. Step 1
  $\text{FD} = \dfrac{\text{frequency}}{\text{class width}}$ .
2. Step 2
  Compute each.
  $\dfrac{8}{10} = 0.8;\ \dfrac{18}{15} = 1.2;\ \dfrac{7}{5} = 1.4$
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
ExtendedGraph or diagram• box plot
Question
A box plot shows: min $4$ , $Q_{1} = 7$ , median $10$ , $Q_{3} = 14$ , max $20$ . State the median, range, and IQR.
Step-by-step solution
1. Step 1
  Direct reads.
  $\text{median} = 10,\ \text{range} = 20 - 4 = 16,\ \text{IQR} = 14 - 7 = 7$
Answer
Median $10$ , range $16$ , IQR $7$ .
4Compare two bar charts
ExtendedGraph or diagram• bar chart
Question
Compare the heights of pupils in two classes shown by two bar charts.
Step-by-step solution
1. 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
CoreGraph or diagram• 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 $\to 4$ , $1$ book $\to 8$ , $2$ books $\to 7$ , $3$ books $\to 4$ , $4$ books $\to 2$ . State the modal number of books and the total number of books read.
Step-by-step solution
1. Step 1
  Modal = bar with greatest frequency. Highest bar is at $1$ book ( $8$ students).
2. Step 2
  Total books = $\sum fx$ .
  $0(4) + 1(8) + 2(7) + 3(4) + 4(2) = 0 + 8 + 14 + 12 + 8 = 42$
Answer
Mode $= 1$ book; total $= 42$ books read.
6Compare data with a dual bar chart
CoreGraph or diagram• 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
1. Step 1
  Compute each pairwise difference: tea $|12-5| = 7$ , coffee $|10-6| = 4$ , juice $|15-12| = 3$ .
2. Step 2
  Biggest difference is for tea.
Answer
Tea, with a difference of $7$ students.
7Draw a frequency polygon
ExtendedGraph or diagram• 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
1. Step 1
  Plot frequency against the MIDPOINT of each class.
2. Step 2
  Midpoints: $5, 15, 25, 35$ . Points: $(5, 3),\ (15, 8),\ (25, 12),\ (35, 5)$ .
3. Step 3
  Join the points with straight line segments.
Answer
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
ExtendedGraph or diagram• 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
1. Step 1
  (a) With equal class widths, frequency on the y-axis is acceptable. Heights: $4, 9, 12, 7, 3$ .
2. Step 2
  (b) Frequency density $= \dfrac{\text{frequency}}{\text{class width}}$ . Divide each by $5$ .
  $\text{FD: } 0.8, 1.8, 2.4, 1.4, 0.6$
Answer
(a) Heights $= 4, 9, 12, 7, 3$ . (b) FDs $= 0.8, 1.8, 2.4, 1.4, 0.6$ .
9Read frequency from a histogram with unequal widths (Challenge)
ChallengeGraph or diagram• 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
1. Step 1
  Frequency $= \text{FD} \times \text{class width}$ .
2. Step 2
  Class $[0, 20)$ : width $20$ .
  $f = 0.6 \times 20 = 12$
3. Step 3
  Class $[20, 30)$ : width $10$ .
  $f = 1.5 \times 10 = 15$
4. Step 4
  Class $[30, 60)$ : width $30$ .
  $f = 0.4 \times 30 = 12$
5. 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
$\text{angle} = \dfrac{\text{frequency}}{\text{total}} \times 360\degree$
When to use
Constructing a pie chart.
Frequency density
$\text{FD} = \dfrac{\text{frequency}}{\text{class width}}$
When to use
Histograms with unequal class widths.
Frequency from area
$\text{frequency} = \text{FD} \times \text{class width}$
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, $Q_{1}$ , median, $Q_{3}$ , 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 $360\degree$
Why it happens
Rounding errors.
How to avoid it
Check the four (or however many) sectors sum to exactly $360\degree$ . 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.