Transcript Mathematics

MATHEMATICS
Bar 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:
Black
Brown
Fair
Ginger
2
11
5
1
• 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…
(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
No. of Guides
12
10
8
6
4
2
0
Black
Brown
Fair
Hair Colour
Ginger
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.
No.of Girl Guides
10
8
6
4
2
0
5
6
7
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
Grouped Data Bar Chart - Example
12
No. of Cubs
10
8
6
4
2
0
2-3
4-5
6-7
Shoe Size
8-10
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 - Example
No. of People
30
25
20
15
10
5
0
120
130
140 150 160
Height (cm)
170
180
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 xaxis may also be drawn.
Continuous Data Bar Chart - Example
No. of People
30
25
20
x
15
x
10
x
x
5
x
0
120
x
130
140 150 160
Height (cm)
170
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.
180
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
Key: Girls
Boys
No. of Students
24
20
16
12
8
4
0
Level 3
Level 4
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
Level 5
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
Percentage of Students
Key: Level 3
Level 4
Level 5
100
80
60
40
20
0
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!
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