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## Precision, Accuracy, Validity, and Reliability

Recall from research methods that there measurements have these four characteristics. A measurement can be more or less precise - how fine a resolution or how many decimal places? A measurement can be accurate (read "near the true value") or inaccurate (aka "wrong"). A measurement can be valid - it measures what we say it measures - or not. And a measurement can be reliable - if you measure again using the same instrument you will get more or less the same result.

## The Elements of Rough Calculations

## Numbers to Know

Basic numbers we should know (in their most basic form)

Ten basic numbers a person in policy should have an intuitive feel for

WorldAbout 7 billion and U.S.About 310 million^{1} population; US legislature435 congress + 100 senators and California legislatureAssembly 80, Senate 40^{2}; number of California counties58; US GDP$13 trillion (thousand billion)^{3}; diameter of earth8,000 miles; median household income in the US$50,000^{4}

Basic sizes. Width of a finger or hand. Ceilings. Doors. Tables. Width of a car.

[http://www.census.gov/ipc/www/popclockworld.html

Orders of magnitude

Communicating Relative Magnitudes

How to approximate a number. Eschew meaningless precision.

Round

Order of magnitude

Scientific notation

Call it something you can remember

If the universe were a baseball diamond type analogies.

Dimensional analysis

Guesstimate

Heuristic

Rule of thumb

Sanity test

How to carry worst/best case values through a calculation

## Exercises

How many movies have you seen? How many bananas have your peeled in your lifetime?

How many hours did you spend on facebook last year?

How many golf balls will fit in this room?

About how much area would we need for a 250 car parking lot?

If the world energy consumption is about 5 x 10^{20} joules^{5} and US is about 1 x 10^{20} joules^{6}, then what is the ratio of US per capita usage to that of the world as a whole?

Announce rather than discard inconvenient uncertainty^{7}

### References

Mitchell N Charity <ude.tim.scl|ytirahcm#ude.tim.scl|ytirahcm> A View from the Back of the Envelope

Wikipedia. "Back of the envelope calculation"

Louisiana Lessons. 1996. Classic Fermi Questions with annotated solutions

Wikipedia. Fermi Problem

mittechtv. 2010. BLOSSOMS - The Art of Approximation in Science and Engineering: How to Whip Out Answers Quickly

Lori Ann White The art of back-of-the-envelope calculations: Students estimate their way through pop culture problems to learn a life skill. Symmetry Online Magazine