mathematics essential to be precise normal, usual. normal has several mathematical meanings. use...
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Mathematics
• Essential to be precise• Normal, usual. Normal has several mathematical
meanings. Use usual for the non-mathematical meaning
• Avoid definite, strict, proper, all, some• Intractable – true meaning if the problem is NP-
hard• Formula, equation – formula is not an equation.
An equation has an equality
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Mathematics
• Equivalent, similar – equivalent means undistinguishable, similar – close
• Element, partition – element is a member of set and not used to mean as part of a subpart of an expression. Partition – used to create subsets
• Average and mean – use arithmetic mean or mean. Average means typical
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Mathematics
• Follow the rules of readability• Use () of appropriate size• Sentences with embedded mathematics should be
structured as if each formula was a simple phrase• Give the type of variable each time use, list L• Displayed formulas should be positive results, so
readers will be not be mislead• Same font size
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Numbers
• Numbers should be usually written as figures, not spelt out.
• Exceptions: – approximate numbers, – numbers up to twenty unless they are literal
values or part of an expression – numbers at the start of sentence– Percentages should always be in figures
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Numbers
• Don’t mix modes– There were between four and 32 processors in each machine.– There were between 4 and 32 processors in each machine
• Numbers never adjacent– There were 14 512 Kb sets.– There were fourteen 512 Kb sets.
• Never omit the 0 in numbers less than 1 • Use same accuracy• Be careful with percentages, explicitly state
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Presentation of Statistics
• Text paragraph
• semitabular form
• tables
• graphics
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Text Presentation• Most common when only a few statistics.
• Writer can direct the reader’s attention to certain numbers or comparisons
• drawback - statistics are submerged in the textA comparison of the four top revenue producing computer software companies from the Fortune 500 survey show that Compuware had the largest % change in revenue from the years 1998-1999. Its growth was 44%. This compares to revenue growth of Microsoft at 36%, Oracle at 24% and in fourth was Computer Associates Intl. at 11%.
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Semitabular Presentation• Just a few figures, figures my be taken form
the text and listed.
• Quantitative comparisons are easier to read in a list
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A comparison of the four top revenue producing computer software companies from the Fortune 500 survey show that Compuware had the largest % change in revenue from the years 1998-1999.
$ millions % Change From 1998
Microsoft 19,747 36
Oracle 8,827 24
Computer Assoc. Intl. 5,253 11
Compuware 1,638 44
Semitabular Presentation Example
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Tabular Presentation
• Superior to text in presenting statistics
• should be accompanied by comments directing the reader’s attention to important figures
• either general or summary
• general tend to be large, complex, detailed and left for the appendix
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Tabular Presentation
• Summary tables contain only a few key pieces of data closely related to the finding
• to make them inviting to the reader, the table designer should omit unimportant details and collapse multiple classifications into composite measures
• contain enough information for the reader to understand its contents
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Tabular Presentation
• Title should explain the subject, how the data are classified, the time period
• if the data does not come from your original research, there should be a source note
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Diagrams
• Are used to show process, structure or state
• Browse relevant papers to show what elements to incorporate and how it should be presented
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Graphs
• Compared with tables, graphs show less information and often only approximate values
• they are more often read and remembered than tables
• many different graphic forms• boxplots, stem-and-leaf displays, histograms, line,
area, pie, bar, pictographs and 3-D graphics
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Graphs
• Each one should be numbered for easy reference
• descriptive caption
• always introduced and discussed within the text
• if not your own, can only be reused with permission of the author and the publisher of the original
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Graphs
• Support the evidence for the hypothesis
• keep simple
• few plotted lines
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Spreadsheet Software
• Allows the user to take control of numbers, manipulating them in ways that would be difficult or impossible otherwise
• graphs - were once very difficult, now part of the software
• can turn the worksheet numbers into charts automatically
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Creating Charts from Numbers
• Offer a variety of basic chart types and options for embellishing charts
• differences among chart types are more that aesthetic
• each chart type is well suited for communicating particular types of information
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0
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1st Qtr 2nd Qtr
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0%10%20%30%40%50%60%70%80%90%
100%
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr
North
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80-10060-8040-6020-400-20
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column bar Stacked barSpider or radar
pieMultiple pie line
bubble
area doughnutscatter
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Pie Chart
• Relative proportions of the parts to a whole
• used with nominal data
• Multiple pie – same as pie but displays another data series
1st Qtr
2nd Qtr
3rd Qtr
4th Qtr
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Line Chart
• Show trends or relationships over time
• show relative distribution of one variable through another (the classic bell-shaped normal curve)
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Example of Line Chart
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Bar Charts/Histograms
• Appropriate when data falls into a few categories.
• Bars can be stacked in a stack chart that shows how proportions of a whole change over time.
• Conventional solution for the display of interval-ratio data
• Note that it shows order to its categories
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Example of a Bar Chart
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Scatter Charts
• Used to discover, rather that display a relationship between two variables
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Example of a Scatter Chart(Graduation Rate vs Crime Rate)
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Others
• Bubble – used to introduce third variable (dots of different sizes) Axis could be sales and profits; bubbles are assets
• Spider, radar – radiating arms are categories; values are distances form centers (shows multiple variables e.g. performance, ratings, progress)
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What about graphs and charts?
• 1992 Presidential election - ( Ross Perot used many graphs)
• One picture is worth a thousand words
• Candidates spoke about trend lines, investments and deficits and did so using colorful charts and graphs.
• voodoo economics
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What about graphs and charts?
• It is simple to create a line graph that drives home the increase in the national debt,
• a bar graph that compares market share for U.S. and foreign automobile manufacturers.
• When you design a graph you have a responsibility to your audience
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The “real” Trend
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Different Axis Calibration
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Guidelines
• Choose the right chart for the job.
• Keep it simple, familiar and understandable
• Strive to reveal the truth, not hide it.
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Spreadsheet Ethics: Making Numbers Lie
• Figures do not lie
• …but, you must be careful about the figures you see, for they are only as accurate as the person who entered them.