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

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

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

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

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

Presentation of Statistics

• Text paragraph

• semitabular form

• tables

• graphics

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%.

Semitabular Presentation• Just a few figures, figures my be taken form

the text and listed.

• Quantitative comparisons are easier to read in a list

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

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

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

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

Diagrams

• Are used to show process, structure or state

• Browse relevant papers to show what elements to incorporate and how it should be presented

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

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

Graphs

• Support the evidence for the hypothesis

• keep simple

• few plotted lines

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

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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column bar Stacked barSpider or radar

pieMultiple pie line

bubble

area doughnutscatter

Pie Chart

• Relative proportions of the parts to a whole

• used with nominal data

• Multiple pie – same as pie but displays another data series

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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)

Example of Line Chart

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

Example of a Bar Chart

Scatter Charts

• Used to discover, rather that display a relationship between two variables

Example of a Scatter Chart(Graduation Rate vs Crime Rate)

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)

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

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

The “real” Trend

Different Axis Calibration

Guidelines

• Choose the right chart for the job.

• Keep it simple, familiar and understandable

• Strive to reveal the truth, not hide it.

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.