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Chapter 2 Organizing/Displaying Data. 2.1 Bar, Circle and Time-Series Graphs. Exploratory Data Analysis. EDA is a method of studying data that uses stem/leaf plots and histograms. It allows for exploration, pattern finding, and observation of extreme values. - PowerPoint PPT Presentation
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Chapter 2Organizing/Displaying
Data2.1 Bar, Circle and Time-
Series Graphs
Exploratory Data Analysis
EDA is a method of studying data that uses stem/leaf plots and histograms. It allows for exploration, pattern finding, and observation of extreme values.
EDA is used when you have general data but are not sure where it might lead or you have few prior assumptions. This is opposed to an experiment where specific data is collected (perhaps with controls) and the observer has particular questions in mind.
Bar Graphs
Segmented bar chart
Bar GraphsVertical or horizontalQuantitative or Qualitative DataBars of uniform Width and uniform spacing betweenLengths represent values of variables, frequency of
occurrence or % of occurrenceLabeled, titled, scalesSometimes scales on sides are general but you will
also see a label on top of a bar to give more specific information
You can change the scale by putting in a “break” on the vertical axis.
Area Principle
The area occupied by a part of a graph should correspond to the magnitude of value it represents. Otherwise, the picture can be misleading even though it is labeled correctly.
15050 200100
Average amount spent on
Holiday Gifts per child
1970
2000
1990
1980
Pareto charts
Circle Graphs (i.e. Pie charts)
Circle Graphs (i.e. Pie Charts)
Each wedge displays proportional part of total population (that is, the percentage that give a particular answer or share a characteristic)
OK for qualitative data.
Time Series Graph (Time Plot)
Time Series Graph (Time Plot)
Data plotted in sequential orderData sequencing is at regular intervals
Time Series Data must be collected for thre same variable for the same subject at regular intervals over a period of time. NASDAQ, NYSE, Rainfall, etc are examples of Time Series Data
Be Careful!!
Make sure your graph is actually saying something…
Some examples of poor graphs
Resources
wme.cs.kent.edu/kimpton/img/b.png
www.nifl.gov/readingprofiles/FT_Introduction.htm
www.statcan.ca/.../power/ch9/bargraph/bar.htm
http://blogs.ittoolbox.com/eai/implementation/archives/now-with-the-pareto-charts-11915
http://www.quadbase.com/espressreport/help/manual/Charting5.html
http://www.newsandtech.com/issues/2007/01-07/nt/01-07_cornish.htm
http://www.statcan.ca/english/edu/power/ch9/piecharts/pie.htm
http://justinsomnia.org/2006/04/bloglines-subscription-stats-just-check-your-httpd-access-logs/
http://www.appiananalytics.com/solutions/report_automation_gallery.htm
http://trmm.gsfc.nasa.gov/trmm_rain/Events/malaysia_time_series.graph.gif
http://news.bbc.co.uk/2/hi/uk_news/education/4276473.stm
http://www.env.gov.bc.ca/wat/wq/trendstuff/9trends/9locations-06.html
http://www.sapdesignguild.org/resources/diagram_guidelines/DIAGRAMS/SegmSR.GIF
2.2 More Data Display
Histograms, Frequency Tables and Contingency Tables
Displaying data by counts
Sometimes there is a lot of data. One way to evaluate data is to list the counts, or how many times a particular answer is given. Imagine if the senior and junior class are asked to choose their favorite car color out of three choices. One way to show that data is a Contingency Table.
Contingency TableAlso called a Two Way Table
A contingency table is a way to display and analyze the relationship between 2 (or more) sets of categorical data.
Red Blue Silver TOTAL
Female 41 62 33 136
Male 59 22 50 131
TOTAL 100 84 88 267
Marginal Total
Marginal
Total
Grand Total
If the data is given as percentages, it may be called a two way frequency table.
Histogram
Bars touch Width of bars represent a quantitative
value (the class)Height indicates frequency (how many
individuals give a response in each particular class)
Some books call the bars bins
Great way to evaluate large quantities of data
Types of Histograms
Symmetric Histogram
Bimodal Histogram
Histogram
0
5
1 1 1 1 1 1 1
Bin
Frequency
Frequency
Uniform/Rectangular Histogram
Skewed Left/Right Histograms
Frequency TableA frequency table is used to organize data for drawing the histogram. Class category or interval
Class Width Width of particular interval
Class Frequency # of tally marks for a particular class
Lower/Upper Class Limit lowest/highest data value that can fit in a particular class
Lower Class Limit + Class Width Smallest Value for next class
Class Boundaries Upper class boundary = UCL + ½ Lower Class Boundary = LCL - ½
Class Midpoint LCL + UCL 2
How to make a Histogram1. Make a frequency table
a) Determine # of classes and class widthb) Find LCL and UCL c) Tally data and find CFd) Find midpointse) Find boundaries
2. Put class Boundaries on horizontal axis, Frequencies on Vertical axis
3. Draw a bar with width extending between Class boundaries, whose height = that particular class frequency
Class Width = Largest Data Value – Smallest Data Value
Desired # of Classes
TI 83
Enter the data by hand into L1 – press “STAT”, “EDIT” and start typing into List 1.
Hit “2nd” “StatPlot”; Turn“ON” the stats plot on Plot1 and select the histogram picture. The TI83 should automatically select the correct list. If it doesn’t, change it by typing in “2nd” and then the list name you want (see above the number keys for the lists)
Hit Graph – you will see a histogram.Go to window and change the xscale to the class
width and that forces it to match your choice of classes.
“Trace” then allows you to see class information.
Excel
Enter all the data by hand.Select “Tools”, “Data Analysis”, “Histogram”
(it might need to install the data analysis package – do it)
Input range is your range of data valuesOutput range is the list that you create
somewhere else in your table that lists the maximum value for each class. This will force it to make the # of classes you want.
Then click OK. It will put it on another worksheet in your file.
Ogive
An Ogive is a dot plot that shows the accumulation at each level.
Resourceshttp://en.wikipedia.org/wiki/Histogram
http://www.statcan.ca/english/edu/power/ch9/histograms/histo.htm
http://www.aivosto.com/project/help/pm-charts.html
www.tcnj.edu/~rgraham/rhetoric/statistics.html
http://www.ncsu.edu/scivis/lessons/variation/varlab2.html
http://mayoresearch.mayo.edu/mayo/research/cpor/tip2.cfm
2.3 Stem/Leaf and Dotplots
What is a stem/leaf display?
Another way to display data in a histogram like method without losing the actual individual data values is a stem/leaf display. It looks like this:
Stem Leaf
Data such as 25, 26, 30, 31, 32, 33, 34, 35, 35, 40, 41, 44 would display like this:
2 5 6
3 0 1 2 3 4 4 5
4 0 1 4
and it is arranged so that the stem is the left digit(s) and the leaves are the right digit(s)
Why a stem/leaf display
Turn that data table sideways and it looks like a histogram – the class with more entries (higher frequency) extends further right.
Lets turn our day 1 pulse exercise into a stem/leaf display.
How to make a stem/leaf display
1. Choose which digits will be the stem and which will be the leaf.
2. Align stems from smallest to largest *3. Place the leaves on line with the
corresponding stem4. Label to indicate representation. i.e.
6│1 = 61 beats per minute.
Dot PlotA dot plot is a little more basic. One axis is the
individuals (or perhaps basic count value), the other is the quantitative data values, and dot represents each data value.
These are the Kentucky Derby winning times from 1875 through 2004.
Any idea why there are two clusters? (Hint: something happened in 1896, and it has nothing to do with steroids)
Blogs
I found this guy’s blog that was really interesting. He was musing over his ipod playlist and wondered how many times some of his songs had played.
“I exported the Library and wrote some python scripts to extract data …It turns out I have 208 unplayed songs in my library, and additionally lots of low single digit playcount songs. Here’s an (ugly excel generated) histogram”
While I was delving around, I figured I would see if theres any correlation between the length of time a song has been in my library, and the number of times it’s been played. The dot plot turned out interesting .
Resourceshttp://www.monkeyatlarge.com/archives/2006/07/
Bock, V., Velleman, P., De Veaux, R, Stats: Modeling the World, 2nd Edition, Boston, Pearson Addison Wesley p. 49