Basic Statistics · the types of data collected ... Column graphs can be combined to compare data...
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Basic Statistics Representing Data - Graphing
Transcript of Basic Statistics · the types of data collected ... Column graphs can be combined to compare data...
Basic Statistics
Representing Data - Graphing
Representing Data
Learning Intentions
Today we will understand:
Graphics don’t just report data theyshow trends and patterns
The graphic used is determined bythe types of data collected
Pie charts, bar graphs, histograms, scatterplots
Image accessed: http://intouchacquisitions.co.uk
Graphing
Is an important way of visually representing data
Provides a significant amount of information
Moves from reporting data to showing trends and patterns
Relationships are more easily identifiedin a graphic representation ascompared to a table
Image accessed: http://www.abcteach.com/documents/clip-art-stick-guy-graphing-grayscale-21480
The graphic used is determined by the types of datacollected
Remember……..
Graphing
Graphing Categorical Variables
Images accessed: https://onlinecourses.science.psu.edu
http://www.statcan.gc.ca
Bar Graph Pie Chart
Figure 1. JCU student demographicsFigure 2. JCU students favourite movie genre
Bar Graph
Date Egg Colour
1 Oct White
1 Oct White
1 Oct Dark Brown
1 Oct White
1 Oct Dark Brown
1 Oct Blue
2 Oct Dark Brown
2 Oct Dark Brown
2 Oct White
2 Oct White
2 Oct White
2 Oct Light Brown
Egg Colour Frequency
White 6
Dark brown 4
Blue 1
Light brown 1
Organise data
Bar Graph
Each category has its own bar with gaps between bars
0
1
2
3
4
5
6
7
White Dark Brown Blue Light Brown
Freq
uen
cy
Egg Colour
Figure 3. The colour of eggs laid during a two day period in October
Bar Graph
Column graphs can be combined to compare data
Date Colour
1 March Blue
1 March Light Brown
1 March Dark brown
1 March Light Brown
1 March Blue
1 March Blue
2 March Blue
2 March Light Brown
2 March White
2 March Light Brown
2 March Blue
2 March Light brown
Egg Colour Frequency
White 1
Dark brown 1
Blue 5
Light brown 5
Organise data
Bar Graph
Column graphs can be combined to compare data
Egg Colour Frequency
White 1
Dark brown 1
Blue 5
Light brown 5
Eggs Laid in October Eggs Laid in March
Egg Colour Frequency
White 6
Dark brown 4
Blue 1
Light brown 1
Bar Graph
0
1
2
3
4
5
6
7
White Dark Brown Blue Light Brown
Freq
uen
cy
Egg Colour
October
March
Figure 4. The colour of eggs laid during a two day period in October and March
Pie Chart
DISCRETE
DISCRETE
The area of the circle is proportional to the frequency
50%
34%
8%8%
White
Dark Brown
Blue
Light Brown
Figure 5. The colour of eggs laid during a two day period in October
Pie Chart
You cannot plot two variables on the same pie chart but you can compare two pie charts
8%8%
42%
42%
White
Dark Brown
Blue
Light Brown
50%
34%
8%8%
White
Dark Brown
Blue
Light Brown
Figure 6. The colour of eggs laid during a two day period in October
Figure 7. The colour of eggs laid during a two day period in March
Histogram
Visual display of frequencies
Quantitative variable – continuous and/or grouped
Shows distribution of all observations in dataset
Describes shape, centre and spread of dataset
Image accessed: http://www.six-sigma-material.com/Histograms.html
Histogram
Figure 8. Distribution of children’s height
Freq
uen
cy
Height (cm)
Image accessed: http://www.abs.gov.au/websitedbs/a3121120.nsf/home/statistical+language+-+frequency+distribution
HistogramFr
equ
ency
Height (cm)
Figure 8. Distribution of children’s height
Histogram
Figure 9. JCU students test scores
0
5
10
15
20
25
30
30
- 3
5
35
- 4
0
40
- 4
5
45
- 5
0
50
- 5
5
55
- 6
0
60
- 6
5
65
- 7
0
70
- 7
5
75
- 8
0
80
- 8
5
85
- 9
0
90
- 9
5
95
- 1
00
Freq
uen
cy (
%)
Test Scores (%)
Frequency can also be expressed as a
percentage of total observations.
Why is this not a good example of a histogram?
Which column would 50 go in? 65? 60? 70?
Show association between two numerical variables
Data plotted as Cartesian (X,Y) coordinates
Suggests relationships between variables
Scatterplot
Pri
ce (
$)
Age (years)
Figure 10. Car price according to age of the car
Image accessed: http://conceptdraw.com/samples/business-charts-area-line-scatter
Scatterplot
Figure 10. Height (cm) and weight (Kg) of JCU students
0
10
20
30
40
50
60
70
80
90
100
140 160 180 200
Wei
ght
(Kg)
Height (cm)
Scatterplot
Can show a “Trend Line” or “Line of Best Fit” on a scatterplot
Quantifies the correlation
y = 0.8247x - 73.891R² = 0.8361
0
10
20
30
40
50
60
70
80
90
100
140 160 180 200
Wei
ght
(Kg)
Height (cm)
Figure 11. Height (cm) and weight (Kg) of JCU students
Correlation Between Variables
Correlation is the relationship between two variables
Correlation is positive when the values increase together
Correlation is negative when one value decreases as the other increases
Image accessed: https://www.mathsisfun.com/data/scatter-xy-plots.html
Graphs Can Be Misleading
Image accessed: http://www.statisticshowto.com/misleading-graphs/
Graphs Can Be Misleading……
Figure 12. Average house price in Cairns
425000
430000
435000
440000
445000
450000
455000
2013 2014 2015
Ave
rage
Ho
use
Pri
ce (
$)
Year
A Better Representation……
0
50000
100000
150000
200000
250000
300000
350000
400000
450000
500000
2013 2014 2015
Ave
rage
Ho
use
Pri
ce (
$)
Year
Figure 13. Average house price in Cairns
Keep It Simple
0
1
2
3
4
5
6
7
Blue Dark Brown Light Brown White
Freq
uen
cy
Egg Colour
Is better than.........
Figure 15. The colour of eggs laid during a two day period in October
Keep It Simple
0
1
2
3
4
5
6
BlueDark Brown
Light BrownWhite
Freq
uen
cy
Egg Colour
Figure 16. The colour of eggs laid during a two day period in October
The simplest representation is best
Graphing Using Excel
Excel is a good data management tool
With some practise, you can produce and edit graphs quickly in Excel
Search the internet and YouTube for videos and tutorials about creating graphs in Excel
Specialised statistical software such as S-Plus will enable you to produce graphs that represent your data with more precision
Lynda.com
You can find and access courses to help with your study through Lynda.com
1) Go to website www.jcu.edu.au
2) Click on “Library”
Lynda.com
3) Go to “Learn”
4) Click on “Lynda.com”
Lynda.com
5) Log in using your jc number and password
Lynda.com
6) Browse the Lynda Library for courses of interest
Lynda.com
7) Search the Lynda Library for courses of interest
8) Select the course that you want from the available course list or search again
Lynda.com
9) When you select a course it opens up like this
Lynda.com
10) It is suggested that you save it to your playlist so that it is easy to find again
Lynda.com
11) To find the course again click on My Courses located on the left side of the screen
Lynda.com
12) When you select My Playlist your saved course(s) appear
http://www.abs.gov.au/websitedbs/a3121120.nsf/home/statistical+language
Image accessed: http://apafolchitorres.org//
References
