What is uneven scales on a bar chart?

The vertical scale must increase in equal steps, or the bars mislead.

Axes and sectors must be labelled, or the diagram cannot be read; labels carry marks.

SingaporeMathsSyllabus dot point

How do we organise data and choose the right statistical diagram to display it?

Organise data into tables and display it using bar charts, pictograms and pie charts, and read information from such diagrams

A focused answer to the N(A)-Level Mathematics outcome on data handling. Frequency tables, bar charts, pictograms and pie charts, how to draw each, and how to read values from them.

Generated by Claude Opus 4.88 min answerUpdated 2026-06-06

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
The answer
Examples in context
Try this

What this dot point is asking

SEAB wants you to organise raw data into tables and display it clearly using bar charts, pictograms and pie charts, and to read information back out of these diagrams. Choosing a sensible diagram and reading it accurately are the core skills, along with the pie-chart angle calculation.

The answer

Organising data in a frequency table

Raw data is first tidied into a frequency table, which lists each category or value alongside how many times it occurs (its frequency). The total of the frequencies is the number of items in the data set. A tally column can help when counting from a list.

Bar charts

A bar chart uses bars of equal width whose heights show the frequencies. The bars are separated by gaps (for categories such as favourite sport). Always label both axes and use an even scale so the heights compare fairly.

Pictograms

A pictogram uses a symbol to represent a fixed number of items, given in a key (for example, one symbol = $5$ books). Part-symbols show smaller amounts. To read a pictogram, multiply the number of symbols by the value in the key.

Pie charts

A pie chart shows how a whole is divided into parts, using sectors of a circle. The whole circle is $360^\circ$ , so each item's share of the angle is:

\text{angle} = \frac{\text{frequency}}{\text{total frequency}} \times 360^\circ

A larger frequency takes a larger slice. To read a pie chart, compare the sizes of the sectors or work back from the angles.

Choosing the right diagram

Bar charts compare separate categories well; pie charts show how a total splits into proportions; pictograms give a quick, friendly picture using a key. The best choice depends on what the data is meant to show.

Worked example

In a class of $40$ students, the way they travel to school is: bus $20$ , walk $12$ , cycle $8$ . Draw a pie chart by finding the angle of each sector.

Step 1: Find the angle per student

The whole pie is $360^\circ$ for $40$ students:

\frac{360^\circ}{40} = 9^\circ \text{ per student}.

Step 2: Find each sector angle

Bus: $20 \times 9^\circ = 180^\circ$ . Walk: $12 \times 9^\circ = 108^\circ$ . Cycle: $8 \times 9^\circ = 72^\circ$ .

Step 3: Check the total

180^\circ + 108^\circ + 72^\circ = 360^\circ,

which confirms the angles are correct.

Step 4: Draw the chart

Use a protractor to mark $180^\circ$ , $108^\circ$ and $72^\circ$ sectors, and label each with its category. The bus sector is exactly half the circle.

Examples in context

Example 1. A school survey. A survey of favourite subjects is best shown as a bar chart, because the subjects are separate categories and the bar heights let you compare them at a glance. The tallest bar shows the most popular subject immediately.

Example 2. A household budget. Splitting a monthly budget into rent, food, transport and savings suits a pie chart, since it shows each part as a slice of the whole. A glance reveals which category takes the biggest share of the total spending.

Try this

Cue. A pie chart category has frequency $10$ out of a total of $40$ . Its angle is $\dfrac{10}{40} \times 360^\circ = 90^\circ$ .
Cue. A pictogram key is one symbol = $4$ cars. A row of $6$ symbols shows $6 \times 4 = 24$ cars.
Cue. Bar heights are $7$ , $5$ and $3$ . The total frequency shown is $7 + 5 + 3 = 15$ .

Exam-style practice questions

Practice questions written in the style of SEAB exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Original4 marksIn a survey of

36

students,

12

chose football,

9

chose badminton,

6

chose swimming and the rest chose running. Find the angle each sport would take on a pie chart for the running sector.

Show worked answer →

First find the number who chose running: $36 - 12 - 9 - 6 = 9$ students.

A pie chart has $360^\circ$ for all $36$ students, so each student is $\dfrac{360^\circ}{36} = 10^\circ$ .

Running: $9 \times 10^\circ = 90^\circ$ .

What markers reward: finding the missing frequency, working out the angle per student (total angle divided by total frequency), and the correct sector angle. Forgetting that the whole pie is $360^\circ$ is the common error.

Original3 marksA pictogram uses one symbol to represent

10

books. One row shows

4

full symbols and one half symbol. How many books does that row represent?

Show worked answer →

Each full symbol is $10$ books, and half a symbol is $5$ books.

$4$ full symbols $= 4 \times 10 = 40$ books.

The half symbol $= \dfrac{1}{2} \times 10 = 5$ books.

Total $= 40 + 5 = 45$ books.

What markers reward: reading the key (one symbol equals $10$ books), counting the full symbols, working out the part symbol correctly, and adding for the total. Reading the key is the essential first step.