MATHEMATICSBar Charts & Vertical Line Graphs

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.

(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

(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

(Basic) Bar Charts - ExampleBlack Brown Fair Ginger

2 11 5 1

Remember: • number the y-axis• label the axes• bars of equal width• gaps between bars!

12

10

8

6

4

2

0Black Brown Fair Ginger

No.

of

Gui

des

Hair Colour

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.

Vertical Line Graphs - Example

• Here are the shoe sizes of the girl guides given in a vertical line graph.

5 6 7 8

10

8

6

4

2

0

No.

of G

irl G

uide

s

Shoe Size

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

Grouped Data Bar Chart - Example12

10

8

6

4

2

0 2-3 4-5 6-7 8-10

No.

of

Cub

s

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 11 + 7 + 2 = 20 cubs altogether.

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).

Continuous Data Bar Chart - Example30

25

20

15

10

5

0120 130 140 150 160 170 180

No.

of

Peo

ple

Height (cm)

This bar chart shows us that:• Most people’s height was between 150-160cm• The least number of people had a height over 170cm• There were 2 + 10 + 14 + 18 + 10 + 1 = 55 people’s heights in the chart

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.

Continuous Data Bar Chart - Example30

25

20

15

10

5

0120 130 140 150 160 170 180

No.

of

Peo

ple

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.

x

x x

x

x

x

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.

Dual Bar Chart - Example

24

20

16

12

8

4

0Level 3 Level 4 Level 5

No.

of

Stu

dent

s

Key: Girls Boys

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 12 + 22 + 15 = 49 girls altogether• There were 10 + 24 + 16 = 50 boys altogether

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.

Composite Bar Chart - Example

100

80

60

40

20

0GIRLS BOYS

Per

cent

age

of S

tude

nts

Key: Level 3 Level 4 Level 5

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!

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: http://app.mymaths.co.uk/351-resource/frequency-tables-and-bar-charts • Online HW: http://app.mymaths.co.uk/351-homework/frequency-tables-and-bar-charts

• Work through the MyMaths lesson and its online homework called Pictograms and Bar Charts which can be found at:

• Lesson: http://app.mymaths.co.uk/352-resource/pictograms-and-bar-charts • Online HW: http://app.mymaths.co.uk/352-homework/pictograms-and-bar-charts

• 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