What you'll learn
This topic covers ways of representing and interpreting data: bar charts, pie charts, pictograms, line graphs and stem-and-leaf diagrams. In this guide you will learn how to draw and read each type, how to choose the right chart for the data, and how to interpret them to answer questions. These are core statistics skills used throughout GCSE and everyday life.
Key terms and definitions
Bar chart — a chart using bars of equal width to show frequencies.
Pie chart — a circle divided into sectors representing proportions.
Pictogram — a chart using symbols, each standing for a number of items.
Line graph — a graph showing how a quantity changes, often over time.
Stem-and-leaf diagram — a way of showing data that keeps the original values.
Core concepts
Bar charts
A bar chart uses bars of equal width with heights showing frequency, and gaps between the bars for categories. Read values off the frequency axis. Dual and composite bar charts let you compare groups side by side or stacked.
Pie charts
A pie chart shows proportions as sectors of a circle, where the whole circle is 360°. To draw one, find each category's angle as (frequency ÷ total) × 360°. To read one, a sector's fraction of 360° gives its share of the total.
Pictograms
A pictogram uses a symbol to represent a set number of items, with a key telling you how many. Part-symbols show fractions of that number. Always check the key before reading values.
Line graphs
A line graph plots points joined by lines, usually showing change over time. The trend (rising, falling, steady) is read from the shape. They suit continuous data such as temperature.
Stem-and-leaf diagrams
A stem-and-leaf diagram splits each value into a stem (e.g. tens) and a leaf (units), keeping the actual data. Ordered leaves make it easy to find the median, mode and range. A key is essential to show what the digits mean.
Worked examples
Example 1: Pie chart angle
Out of 40 people, 10 chose tea. Find the angle for tea.
(10 ÷ 40) × 360 = 90°.
Example 2: Pictogram
A symbol represents 5 cars. How many cars do 3½ symbols show?
3.5 × 5 = 17.5, so 17 or 18 cars (here 17.5 symbols' worth).
Example 3: Stem-and-leaf range
Stem-and-leaf values run from 12 to 47. Find the range.
47 − 12 = 35.
Common mistakes and how to avoid them
Pie angles not summing to 360°. Check all the sector angles add up.
Ignoring the key. Pictograms and stem-and-leaf need the key to read values.
Unequal bar widths. Bars should be equal width with equal gaps.
Joining points on categorical data. Use lines only for continuous data over time.
Forgetting to order the leaves. Order them to find median, mode and range.
Exam technique for Representing Data
Choose the right chart for the data type.
Use (frequency ÷ total) × 360° for pie chart angles.
Read the key on pictograms and stem-and-leaf diagrams.
Order the leaves to find averages and range.
Interpret in context, describing trends and comparisons.
Quick revision summary
Different charts suit different data. A bar chart uses equal-width bars with gaps for categories; dual and composite versions compare groups. A pie chart divides a circle (the whole is 360°) into sectors, each angle being (frequency ÷ total) × 360°. A pictogram uses a symbol for a set number with a key, and part-symbols for fractions. A line graph joins points to show change over time for continuous data. A stem-and-leaf diagram splits values into stems and leaves, keeping the actual data and (when ordered) making the median, mode and range easy to find — always with a key. The common errors are pie angles not totalling 360°, ignoring the key, unequal bar widths, joining categorical points, and unordered leaves. Choose the right chart, calculate pie angles correctly, read the key, order the leaves, and interpret in context.