Bar Charts & Pictograms (Edexcel GCSE Maths: Foundation)

What is a bar chart?

• A bar chart is a visual way to represent discrete data
  • Discrete data is data that can be counted 
    • This can be numerical like shoe sizes in a class
    • Or non-numerical (categorical) like colours of cars down a road
• The horizontal axis shows the different outcomes
• The vertical axis shows the frequency
• The heights of the bars show the frequency
  • Bars should be separated by gaps
  • Bars should have equal widths

What is a dual (comparative) bar chart?

• Dual (or comparative) bar charts compare two data sets on one bar chart
  • The data sets measure the same variable, so use the same scale
  • The bars are in pairs (side-by-side) for each outcome
  • e.g. For comparing the shoe sizes of two year groups

What is a bar-line chart?

• A bar-line chart also shows two data sets on one chart
  • However one data set is represented by a line, and the other by bars
  • This allows two different variables to be shown, with a different scale for each
  • e.g. For showing the monthly temperature (as a line) and the monthly rainfall (as bars) across the year for a location
    • One scale would be in °C, and the other would be in mm

• There are also composite bar charts, which are covered in their own section below

What is a line chart?

• A line chart, or vertical line chart is a visual way to represent discrete data
  
  • Line charts are used for numerical data (rather than categorical data)
    • They are particularly useful when there are lots of different options to show
      e.g.  Results of a test where scores are given as percentages
  • They are different to line graphs, which are used for time-series graphs
• The vertical axis shows the frequency
• The horizontal axis shows the different outcomes

• You can easily identify the mode (most common value) using a line chart
  
  • This will be the outcome with the highest (tallest/longest) line
  • e.g.  In the line chart above, 11 was the modal test score, with a frequency of 7
• You can quickly see how the data is spread using a line chart
  • Lines may be crowded around a particular group of options
  • This may help identify anomalies or outliers in the data
  • e.g.  In the line chart above you can see
    • the majority of the test scores, out of 20, were between 7 and 12
    • one pupil scored 19 out of 20, much higher than anyone else in the class

What is a pictogram?

• A pictogram is an alternative to a bar chart
  • It is used in the same situations
• There are no axes
  • Frequency is represented by symbols
  • A key shows the value of 1 symbol
    • For example, 1 symbol represents a frequency of 2
  • Half and quarter symbols are often used

• The pictogram above shows the shoe sizes of students in a class
  • As 1 picture of a shoe represents 2 students
    • Half a shoe represents 1 student
  • The number of students with a shoe size of 7, is 3

What is a composite bar chart?

• A composite bar chart shows the total frequency for a category as well as the proportions in each category
• For example, the chart below shows the total number of vehicles passing a location at different times
  • The overall height of each bar shows the total number of vehicles
  • The sections within each bar show the proportion of vehicles by type
    • Be careful - it is just the height of each coloured section which shows the frequency, not the whole bar
    • e.g. For 9-9:30 am, there are around 10 bikes, not 80
• Composite bar charts can reveal more information that a regular bar chart
  • e.g. The below chart shows the least traffic in total is between 9:30-10 am, but it is also during this time that the greatest number of lorries are present