Bar Charts, Line Graphs & Pictograms (Edexcel GCSE Statistics)

Revision Note

Bar Charts & Vertical Line Graphs

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

Bar chart showing shoe sizes in a class

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

A dual bar chart showing the number of hot food items and ice creams sold each month for February, March, and April

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

A bar line chart showing both average temperatures and rainfall for different months of the year

What is a vertical line graph?

  • A vertical line graph (or vertical line chart), is a visual way to represent discrete data

    • Vertical line graphs 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

    • Do not confuse these with the line graphs which are used when drawing time series graphs

      • For those, see the 'Time Series Graphs' revision note

  • The vertical axis shows the frequency

  • The horizontal axis shows the different outcomes

vertical line chart
  • 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

Examiner Tips and Tricks

  • If asked to draw a bar chart, find the largest frequency and select a scale which allows it to fit in the space provided

Worked Example

Mr Barr teaches students in Year 7 and Year 8.
He records the number of pets that students in each year have.
His results are shown in the dual bar chart below.
 

A dual bar chart showing the number of pets owned by Year 7 and Year 8 students

(a) Write down the modal number of pets for his Year 7 students.

The modal number (mode) is the number of pets that occurs the most
Visually, this will be the highest bar for Year 7s

The mode for Year 7 is 1 pet

(b) How many Year 8 students does he teach?

Add up all the heights (frequencies) of the Year 8 bars

4 + 8 + 4 + 3 + 0 + 2 = 21

He teaches 21 Year 8 students

Pictograms

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

A pictogram showing shoe sizes in a Year 11 class
  • 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

Composite Bar Charts

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

    Composite bar chart for traffic counts by type and time

Examiner Tips and Tricks

  • It can be useful to annotate each section of the bar with its frequency when working

Worked Example

The composite bar chart below shows the number of ice creams and hot food items sold by a shop each month, for three months.

composite bar chart for worked example

(a) Write down the month in which the most items were sold in total.

The total number of items sold (both ice creams and hot food) is represented by the overall height of the bars

Most items were sold in total in April 

(b) Write down the number of ice creams sold in February.

Ice creams are shown by the striped part of the bar
In February, this part of the bar spans from 600 to 700

700 - 600 = 100
 

In February 100 ice creams were sold

(c) Calculate how many more ice creams were sold in March than in February.

We know that in February 100 ice creams were sold

In March, the striped part of the bar spans from 300 to 600

600 - 300 = 300 ice creams sold in March

Find the difference

300 - 100 = 200
 

In March 200 more ice creams were sold than in February

(d) Find the total percentage of items sold that were ice cream, across the three months. Give your answer to 1 decimal place.

We need to find the total number of ice creams sold across the three months

We already know that the number of ice creams sold in February was 100, and 300 in March

In April, the striped part of the bar spans from 200 to 1000

1000 - 200 = 800 ice creams sold in April

Find the total number of ice creams sold

100 + 300 + 800 = 1200 ice creams sold in total

We need to find the total number of items sold across the three months
Add up the total heights of all the bars

700 + 600 + 1000 = 2300 items sold in total

Find the number of ice creams sold as a percentage of the total number of items

1200 ÷ 2300 = 0.521739... = 52.1739... %

Round to 1 decimal place

52.2 % of all items sold were ice creams

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Roger B

Author: Roger B

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Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.

Dan Finlay

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Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.