1. Bar Charts & Vertical Line Graphs
Mathematics
Bar Charts & Vertical Line Graphs

2. Lesson Objectives The aim of this powerpoint is to help you…
to learn how to produce, read and interpret a variety of bar charts
to learn how to produce, read and interpret vertical line graphs
To learn how to produce a frequency diagram and a frequency polygon.

3. (Basic) Bar Charts
The data (numeric or categoric) is usually labelled along the bottom on the x-axis.
The frequency scale runs up the y-axis – remember to number the lines and not the gaps!
The height of each bar indicates the number of items included in that category or for that data value.
Remember that bars must ALL be of equal width and there must be gaps (of equal width) between the bars

4. (Basic) Bar Charts - Example
Here are the hair colours of the guides in a girl guide group:
Let’s represent this in a bar chart.
First let’s work out the y-axis scale  Brown has the highest frequency of 11. We could use 11 lines going up 1 each time, but this time I think we’ll just use 6 and go up 2 each time…
Black
Brown
Fair
Ginger 2 11 5 1

5. (Basic) Bar Charts - Example
Remember:
number the y-axis
label the axes
bars of equal width
gaps between bars!
Black
Brown
Fair
Ginger 2 11 5 1 12 10 8 6 4 2
No. of Guides
Black Brown Fair Ginger
Hair Colour

6. Vertical Line Graphs
These are the same as basic bar charts except that instead of vertical columns, they have vertical lines.
Like basic bar charts, there should be equal sized gaps between each vertical line.

7. Vertical Line Graphs - Example
Here are the shoe sizes of the girl guides given in a vertical line graph. 10 8 6 4 2
No.of Girl Guides
Shoe Size

8. Bar Charts for Grouped Data
These are the same as basic bar charts except that the labels along the x-axis are ‘groups’ of values.
As before…
The frequency scale runs up the y-axis.
The height of each bar indicates the number of items of that data value or data type.
Bars must ALL be of equal width
There must be gaps (of equal width) between the bars

9. Grouped Data Bar Chart - Example12 10 8 6 4 2
No. of Cubs
Shoe Size
This bar chart shows us that:
NO cubs had a shoe size between 2 and 3 (inclusive)
11 cubs had shoe sizes of 4-5
7 cubs had shoe sizes of 6-7
2 cubs had shoe sizes of 8-10
There were = 20 cubs altogether.

10. Bar Charts for Continuous Data (aka Frequency Diagrams)
These bar charts involve measurements (along the x-axis).
The x-axis is now numbered like a graph (lines not gaps) with a suitable constant scale.
NB. If the jump from zero to the first value along the x-axis is large, you can ‘compress’ the initial part of the scale and represent this with a wiggly line!
As before, the frequency scale runs up the y-axis and the height of each bar indicates the number of items for that ‘class’ of data.
Whilst the bars must ALL be of equal width, there will NOT be any gaps between the bars (unless their frequency is 0).

11. Continuous Data Bar Chart - Example30 25 20 15 10 5
No. of People
Height (cm)
This bar chart shows us that:
Most people’s height was between cm
The least number of people had a height over 170cm
There were = 55 people’s heights in the chart

12. Frequency Polygons
Draw a plot at the top of each bar (in the middle) of a frequency diagram.
Join each plot with a straight line
Where appropriate a line from the x-axis up to the first bar’s plot or from the last bar’s plot to the x-axis may also be drawn.

13. Continuous Data Bar Chart - Example30 25 20 15 10 5
No. of People x x x x x x
Height (cm)
This is our frequency diagram for continuous data.
Let’s put in our plots
We don’t need the bars any more
Let’s join the plots to form the frequency polygon.
We could also put extra lines at the start and end.

14. Dual or Multiple Bar Charts
These types of bar chart allow you to compare two (dual) or more (multiple) sets of data on the same chart.
Each set of data is assigned a different colour or style of shading – a key is required.
The x-axis is labelled with each category or data value and for each of these, the bars for each set of data appear side by side (in the same order).
The gaps only appear between each grouping of bars, ONLY to separate the categories/data values.

15. Dual Bar Chart - Example
Key: Girls Boys 24 20 16 12 8 4
No. of Students
Level Level Level 5
This bar chart shows us that:
More girls than boys gained a level 3
More boys than girls gained a level 4 and a level 5
Most boys (and most girls) gained a level 4
There were = 49 girls altogether
There were = 50 boys altogether

16. Composite or Stacked Bar Charts
These types of bar chart allow you to compare multiple sets of data by comparing the proportions (usually percentages) of each category or value within them.
It is each category or data value that is assigned a different colour or style of shading – a key is needed.
The x-axis is labelled with the title for each set of data (NOT categories/data values, which appear stacked on top of each other in one column).
There are gaps between each column.

17. Composite Bar Chart - Example
Key: Level Level Level 5
Percentage of Students
100 80 60 40 20
GIRLS BOYS
This bar chart shows us that:
A higher proportion of girls than boys gained a level 3
Within the girls, most gained a level 4
Within the boys, most gained a level 5
We do not know HOW MANY of the students gained each level, just the percentages of however many students there were altogether!

18. What next? Print out and read through the notes called Data6.
Work through the MyMaths lesson and its online homework called Frequency Tables and Bar Charts which can be found at:
Lesson:
Online HW:
Work through the MyMaths lesson and its online homework called Pictograms and Bar Charts which can be found at:
Lesson:
Online HW:
Answer the tasks that appear throughout the Data6 notes.
Save and complete the worksheets:
Bar2.xlsx, BarUse1.xlsx, BarUse2.xlsx and HistoBar-S2.xlsx
Now move on to the Data-7 powerpoint