📈 Line chart
Use for data that changes over time, such as monthly temperature. Plot each point, then join them with a line. Time goes on the x axis.
Graphical Skills » Graphs and Charts
What you'll learn this session
Study time: 30 minutes
AQA spec: 3.4.2
- Choose the right graph for the data you have
- Construct line, bar, pie, pictogram, histogram, divided bar and scatter graphs
- Draw and read a population pyramid
- Plot on given axes and interpret graphs, including dispersion graphs
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Unlock This CourseWhy the graph you choose matters
Choosing the right graph makes data clear
Raw numbers in a table are hard to read. A good graph shows the pattern at a glance. A poor choice hides it. In the exam you may have to suggest an appropriate graph for some data, construct one, or plot data on axes that are already drawn for you. You will also be asked to interpret graphs.
Every graph needs the same basics: a title, labelled axes with units, an even scale, and a key if there is more than one set of data.
Key terms:
- Graph: a drawing that shows data so that patterns are easy to see.
- Scale: the equal steps marked along an axis, such as 0, 10, 20, 30.
- Class interval: a group of values, such as 0 to under 20 mm, used to sort data into bars.
- Frequency: how many times a value, or a value in a group, occurs.
Matching the graph to the data
📊 Bar chart
Use for separate categories, such as the number of visitors to five beaches. The bars have gaps between them and are all the same width. Height shows the amount.
🍰 Pie chart
Use to show how a whole is split into parts. Each slice is a share of 360 degrees. It works best with about six slices or fewer.
👤 Pictogram
Uses a small picture to stand for a number of items. A key tells you what one picture is worth. Easy to read, but part-pictures are hard to draw exactly.
▦ Histogram
Use for continuous data sorted into groups, such as pebble lengths. The bars touch and each class interval is the same width. Height shows frequency.
▭ Divided bar
One bar split into sections. Each section is a share of the whole. Useful for comparing how the parts of a whole differ between places.
⋮ Scattergraph
Use to see if two sets of data are linked, such as distance from a town centre and number of shoppers. Each pair of values is one cross. No line joins the crosses.
👥 Population pyramid
A special bar chart showing the age and sex of a population. Covered in its own section below.
Constructing graphs
Follow the same steps each time:
- Pick a scale that uses most of the space, with equal steps. Never squash or stretch part of an axis.
- Label both axes with what they show and the units.
- Plot carefully with a sharp pencil. Mark crosses or dots, then bars or lines.
- Add a title and a key if you need one.
Worked example: a pie chart
A survey of 60 people asked how they travel into a town centre: 30 by car, 15 by bus, 10 on foot and 5 by bike.
Each slice angle = (number ÷ total) × 360.
Car: 30 ÷ 60 × 360 = 180°. Bus: 15 ÷ 60 × 360 = 90°. Walk: 10 ÷ 60 × 360 = 60°. Bike: 5 ÷ 60 × 360 = 30°.
Check: 180 + 90 + 60 + 30 = 360°. Draw them with a protractor, starting from a line drawn from the centre to the top.
Worked example: a pictogram
A key says that one figure stands for 4 people. A row for 10 people needs 2 full figures (8 people) and half a figure (2 people), so 2½ figures. Always work out the key first.
Worked example: a divided bar
Draw one bar 10 cm long to stand for 100%. A group that is 30% of the total gets a section 3 cm long. Put the sections in the same order for every bar, so they are easy to compare.
Histograms with equal class intervals
In a histogram, the numbers on the x axis run on without a break, so the bars touch. For example, the lengths of 40 pebbles might be sorted into 0 to under 20 mm, 20 to under 40 mm, 40 to under 60 mm and 60 to under 80 mm. Each class interval is 20 mm wide, so all the bars are the same width and the height of each bar is the frequency.
The difference from a bar chart: a bar chart shows separate categories (gaps between bars), while a histogram shows a continuous scale (no gaps).
Population pyramids
Population pyramids show how many people are in each age group
A population pyramid shows how many people of each age and sex live in a place. Age groups, such as 0-4, 5-9 and 10-14, go up the middle axis, with the youngest at the bottom. Males are drawn as bars to the left and females to the right. The bars show either the number of people or the percentage of the total, so you must check the scale.
- Wide base: many children and young people.
- Narrow top: few people reach old age.
- Bulge in the middle: many people of working age.
- Wide top: many elderly people.
To construct one, use the same scale on both sides of the middle line. Put the age groups up the middle, youngest at the bottom. Draw the male bars out to the left and the female bars out to the right, starting from the middle line.
To interpret one, read the numbers or percentages for named age groups, compare the two sides, and describe the overall shape.
Worked example: reading a pyramid
A pyramid shows the 0-4 bar reaching 8% for males and 8% for females, and the 80+ bar reaching 1% for each. You would write: "The base is wide with 8% of each sex aged 0-4, and the top is narrow with only 1% aged 80+. This suggests a young population with few elderly people."
Dispersion graphs
A dispersion graph shows how spread out a set of values is. Each value is plotted as a dot along a single scale, and there may be one line of dots for each site. When you interpret one, look at where the dots are bunched together, how far apart the lowest and highest dots are, and whether any dot is far away from the rest.
For example, pebble sizes at two sites could be plotted on the same scale. If one site has dots tightly bunched and the other has dots spread out widely, the first site has more similar pebbles and the second has more varied ones.
Plotting on given axes and interpreting graphs
Sometimes the axes are drawn for you. Then your job is to plot accurately.
- Read the scale first. Work out what each small square is worth.
- Find the x value, then go up to the y value, and mark it clearly.
- On a line chart, join the points with straight lines using a ruler.
- When you read a value off a graph, give the units.
To interpret any graph, use three steps: state the overall pattern, back it up with figures from the graph, and mention anything unusual.
Common mistakes
Leaving gaps between histogram bars. Joining the points on a scattergraph (they should stay as separate crosses). Using a line chart for separate categories. Forgetting axis labels and units. Misreading the scale on a population pyramid, where the bars may show percentages and not numbers. Giving a pie chart angle that does not add up to 360°.
Exam-style question
A student collected data on the number of people in each age group living in a village.
(a) Suggest a graph that would show the age and sex of the people in the village. [1 mark]
(b) The student recorded the lengths of 30 pebbles on the beach near the village. Suggest one graph that would show how the pebble lengths are spread out, and give a reason. [2 marks]
(c) 12 out of 48 people surveyed in the village travel to work by bus. Calculate the angle of the bus slice on a pie chart. [2 marks]
Model answer
(a) A population pyramid. (1)
(b) A histogram (1), because the lengths are continuous data that can be sorted into equal class intervals to show the frequency in each group (1). Accept a dispersion graph, because each length can be plotted as a dot on one scale to show the spread.
(c) 12 ÷ 48 × 360 (1) = 90° (1).
Exam tip
In part (c), write out the calculation as well as the answer. If you make a slip in the arithmetic, you can still earn the method mark.